Some exhibit at exclusive gallery (4)

I believe the answer is:

tate

(Other definitions for tate that I've seen before include "Modern and Britain galleries in London" , "Sugar merchant and art gallery philanthropist, founder, d. 1899" , "Art Gallery donor" , "- - Modern: art gallery" , "Sugar refiner and art gallery founder, d. 1899" .)

I've seen this clue in The Sun.

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