Jumper, possibly, back on top of girl (4)
I believe the answer is:
frog
'jumper' is the definition.
(something which jumps)
'back on top of girl' is the wordplay.
'back' becomes 'fro' (synonyms).
'on top of' says to take the initial letters.
The initial letter of 'girl' is 'g'.
'fro'+'g'='FROG'
'possibly' acts as a link.
(Other definitions for frog that I've seen before include "Common amphibian" , "Leaping amphibian" , "Amphibious hopper" , "in grass?" , "Batrachian" .)