No-one given part: that's offensive (7)
I believe the answer is:
noisome
'offensive' is the definition.
(I know that offensive can be written as noisome)
'no-one given part' is the wordplay.
'one' becomes 'I' (Roman numeral).
'given' says to put letters next to each other.
'part' becomes 'some' (I've seen this before).
'no'+'i'+'some'='NOISOME'
'that's' is the link.
(Other definitions for noisome that I've seen before include "terribly unpleasant" , "Disagreeable, unpleasant" , "noxious smells" , "Smelling bad" , "Foul; putrid" .)