Trot around a study (4)
I believe the answer is:
read
'study' is the definition.
(synonyms)
'trot around a' is the wordplay.
'trot' becomes 'red' (I've seen this in other clues).
'around' means one lot of letters goes inside another.
'red' enclosing 'a' is 'READ'.
(Other definitions for read that I've seen before include "Measure energy or fuel consumption" , "Undertake a course of study" , "Study (subject at university)" , "Check, emend (proof)" , "what follows 18 [OMASUM] in a 17 [RUMINANT]" .)