UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Notification of Redemption of Securities Pursuant to Rule 23c-2

Under the Investment Company Act of 1940

Investment Company Act File No. 811- 21665

Hatteras CORE ALTERNATIVES TEI FUND, L.P.

Name of Registrant

8510 Colonnade Center Drive

Suite 150

Raleigh, North Carolina 27615

Address of Principal Executive Office

The undersigned registered closed-end investment company hereby notifies the Securities and Exchange Commission that it intends to redeem securities of which it is the issuer, as set forth below in accordance with the requirements of Rule 23c-2 under the Investment Company Act of 1940 (the “1940 Act”).

(1) Title of class of securities of Hatteras Core Alternatives TEI Fund, L.P. (the “Fund”) to be redeemed:

Units of limited partnership interest (“Units”)

(2) Date on which the securities are to be redeemed:

As of March 31, 2020

(3) Applicable provisions of the governing instrument pursuant to which the securities are to be redeemed:

The Units are to be redeemed pursuant to Section 4.5(i) of the Fund’s Amended and Restated Limited Partnership Agreement, which provides that the Fund may repurchase Units if, among other things, it would be in the best interests of the Fund—as determined by the Fund’s general partner or directors—for the Fund to repurchase the Units.

(4) If less than all the outstanding securities of a class or series are to be called or redeemed, the principal amount or number of shares and the basis upon which the securities to be called or redeemed are to be selected:

The directors believe it is in the best interest of the Fund to repurchase all outstanding Units that reside in an account containing an amount of Units valued at less than $25,000 (based on net asset value per Unit as of March 31, 2020, after giving effect to the tender offer occurring as of that same date) and/or dissolving pension plans. An account size of $25,000 is less than the minimum account size designated in the Fund’s prospectus, and the directors believe the administrative and operational costs necessary to retain such accounts are not in the best interest of the Fund and the Fund’s limited partners. The Fund intends to repurchase approximately 2.01% of its outstanding Units, having an aggregate estimated net asset value of $1,406,895, representing all of the outstanding Units residing in such accounts.

SIGNATURE

Pursuant to Rule 23c-2 under the 1940 Act, the registrant has caused this notification to be duly executed on its behalf in the City of Raleigh and the State of North Carolina on the 28th day of February, 2020.

Hatteras CORE ALTERNATIVES TEI FUND, L.P.

/s/ Allison Zollicoffer

Name: Allison Zollicoffer

Title: Treasurer