Narrow-minded father gets Carol worried about greeting (9)
I believe the answer is:
parochial
'narrow-minded' is the definition.
(thesaurus)
'father gets carol worried about greeting' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'gets' is a charade indicator (letters next to each other).
'worried' is an anagram indicator (worry can mean to interfere with or disturb).
'about' means one lot of letters goes inside another.
'greeting' becomes 'hi' (hi is a kind of greeting).
'carol' is an anagram of 'rocal'.
'rocal' enclosing 'hi' is 'rochial'.
'pa'+'rochial'='PAROCHIAL'
(Other definitions for parochial that I've seen before include "Having a narrow scope" , "rather restricted" , "Related to local area - narrow" , "Narrow in outlook" .)