Irish county fellow accepting extremely light civic office (9)
I believe the answer is:
mayoralty
'civic office' is the definition.
(a mayor is a civic leader)
'irish county fellow accepting extremely light' is the wordplay.
'irish county' becomes 'mayo' (county in Ireland).
'fellow' becomes 'ray' (man's name).
'accepting' is an insertion indicator (inserted letters are accepted).
'extremely' suggests removing the centre (only the extremes of the word are used).
'light' with its middle taken out is 'lt'.
'ray' enclosing 'lt' is 'ralty'.
'mayo'+'ralty'='MAYORALTY'
(Other definitions for mayoralty that I've seen before include "public office" , "Top town hall office" , "political office" , "civic office" , "Henchard's office" .)