Animal handler's docile rook (5)
I believe the answer is:
tamer
'animal handler's' is the definition.
(I've seen this in another clue)
'docile rook' is the wordplay.
'docile' becomes 'tame' (similar in meaning).
'rook' becomes 'R' (chess abbreviation).
'tame'+'r'='TAMER'
(Other definitions for tamer that I've seen before include "Animal trainer" , "Less arousing, exciting" , "Less wild" , "less offensive?" .)