Gallery giving some artist a test (4)
I believe the answer is:
tate
'gallery' is the definition.
(Tate Modern, Tate Britain etc)
'some artist a test' is the wordplay.
'some' indicates a hidden word (some parts of the word are used).
'TATE' is hidden in the letters of 'artist a test'.
'giving' is the link.
(Other definitions for tate that I've seen before include "Britain/Modern gallery" , "Maurice - - , cricketer 1895-1956" , "Art gallery endowed by a sugar merchant" , "Art Gallery donor" , "Either of two galleries in London" .)