Girl's pen had broken (6)
I believe the answer is:
daphne
'girl's' is the definition.
'pen had broken' is the wordplay.
'broken' indicates an anagram.
'pen'+'had'='penhad'
'penhad' is an anagram of 'DAPHNE'.
(Other definitions for daphne that I've seen before include "Ms du Maurier" , "nymph can be seen" , "Shewd, sharp" , "Name of girl or shrub" , "He'd nap around this shiny shrub" .)