Flier making love in bed (4)
I believe the answer is:
coot
'flier' is the definition.
(coot is a kind of birdanimal)
'love in bed' is the wordplay.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'in' is an insertion indicator.
'bed' becomes 'cot' (cot is a kind of bed).
'o' put inside 'cot' is 'COOT'.
'making' acts as a link.
(Other definitions for coot that I've seen before include "Water bird of rail family" , "Proverbially bald aquatic bird" , "'Bald' water bird" , "Blackish aquatic bird" , "Slow-flying birds, duck-like" .)