Possibly chants a fragment of song (6)
I believe the answer is:
snatch
'a fragment of song' is the definition.
(I've seen this before)
'possibly chants' is the wordplay.
'possibly' indicates anagramming the letters.
'chants' anagrammed gives 'SNATCH'.
(Other definitions for snatch that I've seen before include "A bar or two" , "Bit of a song" , "Grasp hurriedly" , "bit of air" , "Seize quickly and eagerly" .)