Civic dignitary initially respected by Irish county (5)
I believe the answer is:
mayor
'civic dignitary' is the definition.
(I've seen this before)
'initially respected by irish county' is the wordplay.
'initially' indicates taking the first letters.
'by' means one lot of letters go next to another.
'irish county' becomes 'mayo' (county in Ireland).
The initial letter of 'respected' is 'r'.
'r' after 'mayo' is 'MAYOR'.
(Other definitions for mayor that I've seen before include "Elected town/city head" , "City government head" , "Town's elected head" , "Local government head" , "Civic dignitary" .)