Singer has a bit of fun behind field (10)
I believe the answer is:
meadowlark
'singer' is the definition.
(meadowlark is a kind of birdanimal)
'a bit of fun behind field' is the wordplay.
'a bit of fun' becomes 'lark' (I've seen this in another clue).
'behind' means one lot of letters go next to another.
'field' becomes 'meadow' (a meadow is a field).
'lark' after 'meadow' is 'MEADOWLARK'.
'has' is the link.
(Other definitions for meadowlark that I've seen before include "Songbird" , "Bird" .)