Small part of UK rejected crime
I believe the answer is:
sin
'crime' is the definition.
(thesaurus)
'small part of uk rejected' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'part of uk' becomes 'NI' (Northern Ireland).
'rejected' shows that the letters should be reversed in order.
'ni' reversed gives 'in'.
's'+'in'='SIN'
(Other definitions for sin that I've seen before include "Wicked deed" , "Evil" , "Immorality" , "Trespass" , "Depravity" .)