CONSENT OF COUNSEL

We hereby consent to the use of our name and to the references to our Firm under the captions “Fund Counsel” and “Independent Registered Public Accounting Firm and Legal Counsel” in the Prospectus and Statement of Additional Information, respectively, included in the Registration Statement on Form N-2 under the Securities Act of 1933, as amended (the “1933 Act”), of Hatteras Core Alternatives TEI Institutional Fund, L.P. (File Nos. 333-176625 and 811-21985). This consent does not constitute a consent under Section 7 of the 1933 Act, and in consenting to the use of our name and the references to our Firm under such caption we have not certified any part of the Registration Statement and do not otherwise come within the categories of persons whose consent is required under said Section 7 or the rules and regulations of the Securities and Exchange Commission thereunder.

/s/ Drinker Biddle & Reath LLP

Drinker Biddle & Reath LLP

Philadelphia, Pennsylvania

July 2, 2012