A flier gets ahead with her (5)
I believe the answer is:
heron
'a flier' is the definition.
(heron is a kind of birdanimal)
'ahead with her' is the wordplay.
'ahead' becomes 'on' ('on' can be a synonym of 'ahead').
'with' is a charade indicator (letters next to each other).
'on' put after 'her' is 'HERON'.
'gets' is the link.
(Other definitions for heron that I've seen before include "One bird" , "Long-legged long-necked wading bird" , "flier" , "Wading bird with long neck and legs" , "Bird of the Rhone, strangely" .)