English friend entertaining Irish in Muslim state (7)
I believe the answer is:
emirate
'muslim state' is the definition.
(emirate is a type of Islamic state)
'english friend entertaining irish' is the wordplay.
'english' becomes 'e' (abbreviation).
'friend' becomes 'mate' (mate is a kind of friend).
'entertaining' means one lot of letters goes inside another.
'irish' becomes 'IR' (abbreviation).
'mate' placed around 'ir' is 'mirate'.
'e'+'mirate'='EMIRATE'
'in' is the link.
(Other definitions for emirate that I've seen before include "state of Middle East?" , "Meatier (anag) -- Qatar, for example" , "state forbidding alcohol?" , "A Middle East office" , "Arab office" .)