Leaders of Irish Republican Army quite ignorant of one from Baghdad (5)
I believe the answer is:
iraqi
'one from baghdad' is the definition.
(Baghdad is in Iraq)
'leaders of irish republican army quite ignorant' is the wordplay.
'leaders of' indicates taking the first letters.
The first letters of 'irish republican army quite ignorant' is 'IRAQI'.
'of' acts as a link.
(Other definitions for iraqi that I've seen before include "Middle Easterner" , "Arab national" , "From Basra, possibly" , "Resident of Baghdad, say" , "native of troubled land" .)