Pets trained by a German sculptor (7)
I believe the answer is:
epstein
'sculptor' is the definition.
(Jacob Epstein)
'pets trained by a german' is the wordplay.
'trained' indicates an anagram (train can mean to shape or manipulate).
'by' is a charade indicator (letters next to each other).
'a german' becomes 'ein' ('a' in German).
'pets' with letters rearranged gives 'epst'.
'epst'+'ein'='EPSTEIN'
(Other definitions for epstein that I've seen before include "old artist" , "Sir Jacob ..., sculptor noted for his statues of the famous" , "British sculptor, d. 1959 - Beatles manager, d. 1967" , "A rock band manager" , "pop group's manager" .)