Motive for arson, possibly, around the end of June (6)
I believe the answer is:
reason
'motive' is the definition.
(reason is a kind of motive)
'arson possibly around the end of june' is the wordplay.
'possibly' indicates an anagram.
'around' indicates putting letters inside.
'the end of' says to take the final letters.
The last letter of 'june' is 'e'.
'arson' with letters rearranged gives 'rason'.
'rason' enclosing 'e' is 'REASON'.
'for' is the link.
(Other definitions for reason that I've seen before include "Cause, justification" , "Logic and rationality" , "Cause or motive" , "Cause; think logically" , "Capacity for rational thought" .)