This person backed Irish ruler (4)
I believe the answer is:
emir
'ruler' is the definition.
(emir is a kind of ruler)
'this person backed irish' is the wordplay.
'this person' becomes 'me' (I've seen this in other clues**).
'backed' says the letters should be written in reverse.
'irish' becomes 'ir' (abbreviation).
'me' in reverse letter order is 'em'.
'em'+'ir'='EMIR'
(Other definitions for emir that I've seen before include "Eastern chieftain" , "Islamic ruler" , "Arabic ruler" , "Middle Eastern ruler" , "Eastern ruler in mire" .)