Mother possibly, or father, torn apart (6)
I believe the answer is:
parent
'mother possibly' is the definition.
(mother is a kind of parent)
'father torn apart' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'torn apart' becomes 'rent' (past tense of 'rend', to tear or rip).
'pa'+'rent'='PARENT'
'or' acts as a link.
(Other definitions for parent that I've seen before include "Pa or Ma" , "Mum or dad" , "Rear" , "old man?" , "Procreator" .)