Founding Father, fellow causing annoyance mostly (8)
I believe the answer is:
franklin
'founding father' is the definition.
(US founding father Benjamin Franklin)
'fellow causing annoyance mostly' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'causing annoyance' becomes 'rankling' (I've seen this before).
'mostly' means to remove the last letter (most but not all of the word).
'rankling' with its final letter taken off is 'ranklin'.
'f'+'ranklin'='FRANKLIN'
(Other definitions for franklin that I've seen before include "Tale-bearer" , "Benjamin or Roosevelt" , "One with a tale to tell" , "Statesman" , "old landowner" .)