EXHIBIT (N)

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the use in this Post-Effective Amendment No. 3 to Registration Statement No. 333-176624 on Form N-2 of Hatteras Core Alternatives TEI Fund, L.P. of our report dated May 30, 2013, relating to the financial statements of Hatteras Core Alternatives Fund, L.P, Hatteras Core Alternatives TEI Fund, L.P., Hatteras Core Alternatives Institutional Fund, L.P., and Hatteras Core Alternatives TEI Institutional Fund, L.P. (collectively the “Funds”), appearing in the Statement of Additional Information, which is part of the Registration Statement. We also consent to the incorporation by reference in the Post-Effective Amendment of such report appearing in the Annual Report on Form N-CSR of the Funds for the year ended March 31, 2013. We also consent to the use in the Post-Effective Amendment of our report dated May 30, 2013, relating to the financial statements of Hatteras Master Fund, L.P. appearing in the Statement of Additional Information, and to the incorporation by reference in the Post-Effective Amendments of such report appearing in the Annual Report on Form N-CSR of Hatteras Master Fund, L.P. for the year ended March 31, 2013. We also consent to the references to us under the headings “Financial Highlights” and “Independent Registered Public Accounting Firm” in the Prospectus, and “Committees” and “Independent Registered Public Accounting Firm and Legal Counsel” in the Statement of Additional Information, which is part of the Registration Statement.

DELOITTE & TOUCHE LLP

Philadelphia, Pennsylvania

July 17, 2013