Reptile giving a girl a lot of trouble (9)
I believe the answer is:
alligator
'reptile' is the definition.
(alligator is a kind of reptile)
'a girl a lot of trouble' is the wordplay.
'of trouble' indicates anagramming the letters (I've seen this in other clues).
'girl'+'a'+'lot'='girlalot'
'girlalot' anagrammed gives 'lligator'.
'a'+'lligator'='ALLIGATOR'
'giving' acts as a link.
(Other definitions for alligator that I've seen before include "Reptile of the Florida Everglades" , "one bites voraciously?" , "predator" , "It could be in zoo" , "Vicious attacker" .)