Some of them irritated a Muslim ruler (4)
I believe the answer is:
emir
'muslim ruler' is the definition.
(type of ruler in some Muslim countries)
'some of them irritated a' is the wordplay.
'some of' indicates a hidden word.
'EMIR' is hidden within 'them irritated a'.
(Other definitions for emir that I've seen before include "Middle Eastern ruler" , "Ruler in the Middle East and mire" , "Arabian ruler" , "Top man" , "Arab chieftain" .)