Flier’s clothes keep in warmth (8)
I believe the answer is:
wheatear
'flier's' is the definition.
(wheatear is a kind of birdanimal)
'clothes keep in warmth' is the wordplay.
'clothes' becomes 'wear' (synonyms).
'keep in' is an insertion indicator.
'warmth' becomes 'heat' (synonyms).
'wear' placed around 'heat' is 'WHEATEAR'.
(Other definitions for wheatear that I've seen before include "Migrant's passion" , "Songbird" , "singer" , "bird" .)