Elon Musk initially annoyed Islamic state (7)
I believe the answer is:
emirate
'islamic state' is the definition.
(as in the United Arab Emirates)
'elon musk initially annoyed' is the wordplay.
'initially' says to take the initial letters.
'annoyed' becomes 'irate' (I've seen this before).
The initial letters of 'elon musk' is 'em'.
'em'+'irate'='EMIRATE'
(Other definitions for emirate that I've seen before include "Such as Abu Dhabi or Dubai" , "Muslim government" , "chieftain's office" , "A Middle East office" , "Arab territory" .)