Artist giving tense exploit a going-over (5)
I believe the answer is:
klimt
'artist' is the definition.
(I know that Klimt is a painter)
'giving tense exploit a going-over' is the wordplay.
'giving' means one lot of letters go next to another.
'tense' becomes 't' (grammatical abbreviation).
'exploit' becomes 'milk' (to milk something is to exploit its potential).
'a going over' says the letters should be written in reverse.
't' next to 'milk' is 'tmilk'.
'tmilk' back-to-front is 'KLIMT'.
(Other definitions for klimt that I've seen before include "Gustav - - , Austrian symbolist" , "Gustav -, nineteenth to twentieth century Austrian painter" , "Austrian painter influenced by Art Nouveau" , "Austrian artist" .)