Go round or up to an art gallery (6)
I believe the answer is:
rotate
'go round' is the definition.
(I've seen this before)
'or up to an art gallery' is the wordplay.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'to an art gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'or' backwards is 'ro'.
'ro'+'tate'='ROTATE'
(Other definitions for rotate that I've seen before include "wheel" , "Make to spin around" , "Alternate" , "'Er, to a T? (anag)" , "Go round and round" .)