Crossword Genius

Entering an American state quietly, I can't abide an Islamic one (9)

Ross

I believe the answer is:

caliphate

I'm a little stuck... Click here to teach me more about this clue!

'islamic one' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.

'entering an american state quietly i can't abide' is the wordplay.
'entering' means one lot of letters goes inside another.
'an american state' becomes 'cal' (short for California. I am not sure about the 'american' bit.).
'quietly' becomes 'p' (p for piano and quiet).
'can't abide' becomes 'hate' (I've seen this in another clue).
'cal'+'p'='calp'
'calp' going around 'i' is 'calip'.
'calip'+'hate'='CALIPHATE'

'an' is the link.

Can you help me to learn more?

(Other definitions for caliphate that I've seen before include "Type of government" , "religious office" .)

I've seen this clue in The Independent.
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