Accepted one part that's not suitable (5)
I believe the answer is:
inapt
'not suitable' is the definition.
(I've seen this before)
'accepted one part' is the wordplay.
'accepted' becomes 'in' (I've seen this in other clues).
'one' becomes 'a' (a thing is one thing).
'part' becomes 'pt' (abbreviation).
'in'+'a'+'pt'='INAPT'
'that's' acts as a link.
(Other definitions for inapt that I've seen before include "It's clumsy" , "not seemly" , "Inappropriate" , "badly judged" , "Out of place" .)