Revolutionary leader's old rival upset by bishop (7)
I believe the answer is:
bolivar
'revolutionary leader's' is the definition.
(I've seen this before)
'old rival upset by bishop' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'upset' indicates an anagram.
'by' says to put letters next to each other.
'bishop' becomes 'b' (abbreviation used in chess).
'rival' is an anagram of 'livar'.
'o'+'livar'='olivar'
'olivar' put after 'b' is 'BOLIVAR'.
(Other definitions for bolivar that I've seen before include "Simon --, South American liberator" , "Revolutionary leader" , "Foreign brass" , "Founder of Bolivia" , "Basic unit of money in Venezuela" .)