Bit of fun for a flier (4)
I believe the answer is:
lark
I believe this clue is a double definition.
'bit of fun' is the first definition.
(I've seen this in another clue)
'flier' is the second definition.
(lark is a type of bird)
'for a' acts as a link.
(Other definitions for lark that I've seen before include "Soaring bird" , "Bird that sings on the wing" , "High-flying songbird" , "Early bird with morning song" , "Early riser" .)