Go round art centre, old gallery (6)
I believe the answer is:
rotate
'go round' is the definition.
(thesaurus)
'art centre old gallery' is the wordplay.
'centre' indicates the central letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'gallery' becomes 'tate' (I've seen this before).
The central letter of 'art' is 'r'.
'r'+'o'+'tate'='ROTATE'
(Other definitions for rotate that I've seen before include "Go around" , "roll" , "Turn round" , "Pivot" , "Pirouette" .)