Exhibit 99.906CERT

CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, David B. Perkins, Principal Executive Officer of Hatteras Core Alternatives TEI Institutional Fund, LP, certify to the best of my knowledge that:

1.The N-CSR of the registrant for the period ended September 30, 2016 (the “Report”) fully complies with the requirements of Section 15(d) of the Securities Exchange Act of 1934; and

2.The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the registrant.

/s/ David B. Perkins

David B. Perkins, President

(Principal Executive Officer)

Date: December 8, 2016

This certification is being furnished to the Securities and Exchange Commission pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as amended, and 18 U.S.C. §1350 and is not being filed as part of Form N-CSR with the Securities and Exchange Commission.

A signed original of this written statement required by Section 906 has been provided to Hatteras Core Alternatives TEI Institutional Fund, LP and will be retained by Hatteras Funds LP, and furnished to the Securities and Exchange Commission or its staff upon request.

CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, R. Lance Baker, Principal Financial Officer of Hatteras Core Alternatives TEI Institutional Fund, LP, certify to the best of my knowledge that:

1.The N-CSR of the registrant for the period ended September 30, 2016 (the “Report”) fully complies with the requirements of Section 15(d) of the Securities Exchange Act of 1934; and

2.The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the registrant.

/s/ R. Lance Baker

R. Lance Baker, Treasurer

(Principal Financial Officer)

Date: December 8, 2016

This certification is being furnished to the Securities and Exchange Commission pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as amended, and 18 U.S.C. §1350 and is not being filed as part of Form N-CSR with the Securities and Exchange Commission.

A signed original of this written statement required by Section 906 has been provided to Hatteras Core Alternatives TEI Institutional Fund, LP and will be retained by Hatteras Funds LP, and furnished to the Securities and Exchange Commission or its staff upon request.