The London tourist attraction, which exhibits British art from 1500 through to the present day, has reportedly seen a drop in awareness because of the popularity of its contemporary sister gallery, Tate Modern.
It is now hunting for a creative agency to develop a brand campaign that will boost its profile.
Tate Britain, which was originally known as the London Tate Gallery, was given a new identity before the opening of the Tate Modern in 2000.
The launch was accompanied by a campaign by TBWA\London that sought to capture the spirit and values of the new Tate with the line: "Look again. Think again."
It led to Tate Britain being seen as the gallery for the art connoisseur, with Tate Modern positioned as the destination for the more adventurous tourist.
TBWA held the account from 1997 to 2000, when it moved to Miles Calcraft Briginshaw Duffy.
Tate Modern has become one of the most popular art galleries in the world and the third-most visited tourist attraction in Britain.