Exhibit 99.(n)

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the use in this Post-Effective Amendment No. 1 to Registration Statement No. 333-199043 on Form N-2 of Hatteras Core Alternatives TEI Fund, L.P. of our reports dated June 1, 2015, 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”) and Hatteras Master Fund, L.P., appearing in the Statement of Additional Information, which is part of the Registration Statement and to incorporation by reference in the Post-Effective Amendment of such reports appearing in the Annual Report on Form N-CSR for the year ended March 31, 2015.  We also consent to the references to us under the headings “Financial Highlights” 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.

/s/ DELOITTE & TOUCHE LLP

Philadelphia, Pennsylvania

July 14, 2015