Female apt to turn around and quarrel (4)
I believe the answer is:
tiff
'quarrel' is the definition.
(tiff is a kind of quarrel)
'female apt to turn around' is the wordplay.
'female' becomes 'f' (abbreviation).
'apt' becomes 'fit' (I've seen this before).
'to turn around' says the letters should be written in reverse (I've seen 'turning around' mean this).
'f'+'fit'='ffit'
'ffit' reversed gives 'TIFF'.
'and' acts as a link.
(Other definitions for tiff that I've seen before include "Quarrel (colloq.)" , "(Lovers') quarrel" , "Mild quarrel" , "A petty quarrel or difference" , "causing quarrel" .)