One's a bit put out, having to be deferential (8)
I believe the answer is:
obeisant
'to be deferential' is the definition.
(thesaurus)
'one's a bit put out' is the wordplay.
'put out' is an anagram indicator.
'ones'+'a'+'bit'='onesabit'
'onesabit' is an anagram of 'OBEISANT'.
'having' acts as a link.
(Other definitions for obeisant that I've seen before include "Curtsying" , "Showing deferential respect" , "showing deference" , "Being submissive" , "obsequious" .)