Female breaking rules Rome formulated is contrite (10)
I believe the answer is:
remorseful
'contrite' is the definition.
('remorseful' can be a synonym of 'contrite')
'female breaking rules rome formulated' is the wordplay.
'female' becomes 'f' (abbreviation).
'breaking' is an insertion indicator.
'formulated' is an anagram indicator.
'rules'+'rome'='rulesrome'
'rulesrome' anagrammed gives 'remorseul'.
'f' put into 'remorseul' is 'REMORSEFUL'.
'is' is the link.
(Other definitions for remorseful that I've seen before include "Showing deep regret" , "Chastened" , "Contrite" , "Sorry" .)