Popular splinter group owning Republican breach (10)
I believe the answer is:
infraction
'breach' is the definition.
(a breach of the rules)
'popular splinter group owning republican' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'splinter group' becomes 'faction' (as in a faction of an organisation).
'owning' indicates putting letters inside.
'republican' becomes 'r' (abbreviation).
'faction' going around 'r' is 'fraction'.
'in'+'fraction'='INFRACTION'
(Other definitions for infraction that I've seen before include "Violation of law" , "transgression" , "Breach of agreement" .)