Home rule divides party giving offence (10)
I believe the answer is:
infraction
'offence' is the definition.
(I know that infraction is a type of offence)
'home rule divides party' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'rule' becomes 'r' (abbreviation for rule).
'divides' is an insertion indicator (inserted letters create a division or opening).
'party' becomes 'faction' ().
'r' put within 'faction' is 'fraction'.
'in'+'fraction'='INFRACTION'
'giving' acts as a link.
(Other definitions for infraction that I've seen before include "Violation of law" , "Breach of agreement" , "transgression" .)