Sort of order British installed in restored caliphate (10)
I believe the answer is:
alphabetic
'sort of order' is the definition.
(alphabetical order)
'british installed in restored caliphate' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'installed in' is an insertion indicator.
'restored' indicates an anagram (I've seen this in other clues).
'caliphate' anagrammed gives 'alphaetic'.
'b' put inside 'alphaetic' is 'ALPHABETIC'.
(Other definitions for alphabetic that I've seen before include "showing certain things in their natural order?" , "in conventional order" , "like characters in a demo" , "with a first, etc" .)