Exhibit 99.1

Insperity and Starboard Reach Agreement on Board Composition and Establish New Independent Advisory Committee

HOUSTON – March 23, 2015 – Insperity, Inc. (NYSE: NSP), a leading provider of human resources and business performance solutions for America’s best businesses, today announced that its Board of Directors has reached an agreement with Starboard Value LP (together with its affiliates, “Starboard”), its largest shareholder, in advance of the Company’s 2015 annual meeting of shareholders.

Under the terms of the agreement, Starboard has agreed to vote all of its shares at the upcoming annual meeting in favor of the Company’s incumbent Class II directors, who are Paul Sarvadi, Chairman and Chief Executive Officer, Carol Kaufmann, Lead Independent Director, and Austin Young, Chairman of the Finance and Risk Management Committee. The agreement also calls for the immediate appointment of two new directors to the Board of Directors (Norman Sorensen and Peter Feld, who will be the only nominee affiliated with Starboard) and the later appointment of a third director nominated by Starboard. Two existing directors, Paul Lattanzio and Jack Fields, who had decided not to seek re-election when their terms expire in 2016, have announced their decisions to depart from the Board immediately following the 2015 annual meeting. In addition, Starboard has agreed to customary standstill restrictions.

Pursuant to the agreement, the Board has created a new independent advisory committee to review the Company’s business and make recommendations to the Board regarding capital allocation, expenses and targeted ranges for Adjusted EBITDA Margins, as defined in the agreement, while taking into consideration the Company’s risk profile and the potential impact of any recommendations on the Company’s business model and strategic plan. The new committee consists of two current independent directors and two Starboard nominees, including Mr. Feld, who chairs the committee. The committee will evaluate Insperity’s cost structure and

recommend targeted ranges for Adjusted EBITDA Margins for fiscal years 2015 and 2016, which the Board will have the right to review and approve. Subject to the approval of such recommendations by the Board, the Company will issue a press release or public announcement discussing such approved recommendations no later than the second quarter fiscal year 2015 earnings announcement.

“This agreement represents the best possible outcome for all of our shareholders. We look forward to working with the new directors toward our common goal of enhancing long-term shareholder value and continuing our strong business momentum,” said Mr. Sarvadi. “I want to express my sincere gratitude to Mr. Lattanzio and Mr. Fields for their many years of commitment and distinguished service on the Board, which helped oversee our recently completed business transformation.”

Peter Feld, on behalf of Starboard, stated: “As the Company’s largest shareholder, we recognize the value of Insperity’s platform and are pleased to join the Board. We believe the addition of new independent directors will bring a fresh perspective to the boardroom and we look forward to working constructively with the incumbent Board members to enhance shareholder value.”

The new directors qualify as “independent” directors under the New York Stock Exchange’s governance rules. Mr. Sorensen has been appointed as a Class II director and the Board unanimously recommends that shareholders elect him at the upcoming annual meeting. Mr. Feld has been and the future nominee of Starboard will be appointed as Class I directors and will be subject to the election by shareholders at the annual meeting in 2017. One or more new directors will be named to serve on each of the Board’s existing committees.

Additionally, the Company has been in the process of exploring alternatives regarding the Company’s two aircraft, including the possible sale of the aircraft. However, pursuant to the agreement with Starboard, the Company is announcing its intent to commence activities to market the aircraft for sale. The Company is in the process of initiating an appraisal of the aircraft to determine the current market values. In the event that the current market values are less than the Company’s book value of the aircraft, then the Company would incur an impairment loss equal to the difference.

The agreement will be filed by the Company with the U.S. Securities and Exchange Commission as an exhibit to a Current Report on Form 8-K.

Peter Feld is a Managing Member and Head of Research of Starboard Value LP, a New York-based investment adviser with a focused and fundamental approach to investing in publicly traded U.S. companies (“Starboard Value LP”), a position he has held since April 2011. From November 2008 to April 2011, Mr. Feld served as a Managing Director of Ramius LLC and a Portfolio Manager of Ramius Value and Opportunity Master Fund Ltd. From February 2007 to November 2008, Mr. Feld served as a Director at Ramius LLC. Since October 2014, Mr. Feld has served as a member of the board of directors of Darden Restaurants, Inc. (“Darden”), a full service restaurant company. Mr. Feld has also served as a member of the board of directors of Tessera Technologies, Inc., which develops, invests in, licenses and delivers innovative miniaturization technologies and products for next-generation electronic devices, since June 2013. Mr. Feld previously served on the board of directors of Integrated Device Technology, Inc., a company which designs, develops, manufactures and markets a range of semiconductor solutions for the advanced communications, computing and consumer industries, from June 2012 until February 2014. Mr. Feld received a BA in economics from Tufts University.

Norman Sorensen formerly served as Chairman of the International Insurance Society, Inc., a professional organization for the insurance industry, from January 2010 until June 2013. Mr. Sorensen has served as a director of the International Insurance Society, Inc. since January 2005. Previously, from November 2011 until December 2012, he was Chairman of the International Advisory Council of Principal Financial Group, Inc., a global financial investment management company. He was Chairman of Principal International, Inc., serving from June 2011 to October 2012, and President and CEO of International Asset Management and Accumulation of Principal International, Inc., serving from January 2001 to June 2011. Mr. Sorensen has served as a director

of Encore Capital Group, Inc., a consumer banking company, since November 2011. Mr. Sorensen also served as a director of Sara Lee Corporation, an American consumer-goods company, from January 2007 to November 2011. He has served as Executive Vice President of both Principal Financial Group Inc. and Principal Life Insurance Company, a life insurance company, since January 2007, as well as having held a number of other senior management positions since 1998. Mr. Sorensen also served as Chairman of the U.S. Coalition of Service Industries, a leading forum for the services sector, from January 2003 to March 2005. Mr. Sorensen served as a senior executive of American International Group, Inc., an insurance services company, from September 1989 to December 1998. He also formerly served as Chairman and director of DE Master Blenders, from December 2011 until September 2013.

About Insperity

Insperity, a trusted advisor to America’s best businesses for more than 28 years, provides an array of human resources and business solutions designed to help improve business performance. Insperity^®Business Performance Advisors offer the most comprehensive suite of products and services available in the marketplace. Insperity delivers administrative relief, better benefits, reduced liabilities and a systematic way to improve productivity through its premier Workforce Optimization^® solution. Additional company offerings include Human Capital Management, Payroll Services, Time and Attendance, Performance Management, Organizational Planning, Recruiting Services, Employment Screening, Financial Services, Expense Management, Retirement Services and Insurance Services. Insperity business performance solutions support more than 100,000 businesses with over 2 million employees. With 2014 revenues of $2.4 billion, Insperity operates in 57 offices throughout the United States. For more information, visit http://www.insperity.com.

About Starboard Value LP

Starboard Value LP is a New York-based investment adviser with a focused and fundamental approach to investing in publicly traded U.S. companies. Starboard invests in deeply undervalued companies and actively engages with management teams and boards of directors to identify and execute on opportunities to unlock value for the benefit of all shareholders.

The statements contained herein that are not historical facts are forward-looking statements within the meaning of the federal securities laws (Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934). You can identify such forward-looking statements by the words “expects,” “intends,” “plans,” “projects,” “believes,” “estimates,” “likely,” “possibly,” “probably,” “goal,” “opportunity,” “objective,” “target,” “assume,” “outlook,” “guidance,” “predicts,” “appears,” “indicator” and similar expressions. Forward-looking statements involve a number of risks and uncertainties. In the normal course of business, Insperity, Inc., in an effort to help keep our stockholders and the public informed about our operations, may from time to time issue such forward-looking statements, either orally or in writing. Generally, these statements relate to business plans or strategies, projected or anticipated benefits or other consequences of such plans or strategies, or projections involving anticipated revenues, earnings, unit growth, profit per worksite employee, pricing, operating expenses or other aspects of operating results. We base the forward-looking statements on our expectations, estimates and projections at the time such statements are made. These statements are not guarantees of future performance and

involve risks and uncertainties that we cannot predict. In addition, we have based many of these forward-looking statements on assumptions about future events that may prove to be inaccurate. Therefore, the actual results of the future events described in such forward-looking statements could differ materially from those stated in such forward-looking statements. Among the factors that could cause actual results to differ materially are: (i) adverse economic conditions; (ii) regulatory and tax developments and possible adverse application of various federal, state and local regulations; (iii) the ability to secure competitive replacement contracts for health insurance and workers’ compensation contracts at expiration of current contracts; (iv) increases in health insurance costs and workers’ compensation rates and underlying claims trends, health care reform, financial solvency of workers’ compensation carriers, other insurers or financial institutions, state unemployment tax rates, liabilities for employee and client actions or payroll-related claims; (v) failure to manage growth of our operations and the effectiveness of our sales and marketing efforts; (vi) the competitive environment in the PEO industry may impact growth and/or profitability; (vii) our liability for worksite employee payroll, payroll taxes and benefits costs; (viii) our liability for disclosure of sensitive or private information; (ix) our ability to integrate or realize expected returns on our acquisitions; (x) failure of our information technology systems; (xi) an adverse final judgment or settlement of claims against Insperity; and (xii) the actions of certain stockholders that could disrupt our business. These factors are discussed in further detail in Insperity’s filings with the U.S. Securities and Exchange Commission. Any of these factors, or a combination of such factors, could materially affect the results of our operations and whether forward-looking statements we make ultimately prove to be accurate.

Except to the extent otherwise required by federal securities law, we do not undertake any obligation to update our forward-looking statements to reflect events or circumstances after the date they are made or to reflect the occurrence of unanticipated events.

Important Additional Information

Insperity, its directors and certain of its executive officers and employees may be deemed to be participants in the solicitation of proxies from Insperity stockholders in connection with the matters to be considered at Insperity’s 2015 annual meeting. Insperity plans to file a proxy

statement and proxy card with the U.S. Securities and Exchange Commission in connection with the 2015 annual meeting. INSPERITY STOCKHOLDERS ARE STRONGLY ENCOURAGED TO READ THE 2015 PROXY STATEMENT AND ACCOMPANYING PROXY CARD (INCLUDING ANY AMENDMENTS OR SUPPLEMENTS THERETO) WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Information regarding the identity of potential participants, and their direct or indirect interests, by security holdings or otherwise, will be set forth in the proxy statement and other materials to be filed with the SEC in connection with the 2015 annual meeting. Stockholders will be able to obtain the proxy statement, any amendments or supplements to the proxy statement and other documents filed by Insperity with the SEC for no charge at the SEC’s website at http://www.sec.gov/. Copies will also be available at no charge at the Investor Relations section of our corporate website at http://www.insperity.com.

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