Muslim leader has a cheek, breaking into church (6)
I believe the answer is:
caliph
'muslim leader' is the definition.
(I've seen this before)
'a cheek breaking into church' is the wordplay.
'cheek' becomes 'lip' (both can mean insolence or rudeness).
'breaking into' means one lot of letters goes inside another.
'church' becomes 'ch' (abbreviation on maps etc).
'a'+'lip'='alip'
'alip' placed inside 'ch' is 'CALIPH'.
'has' is the link.
(Other definitions for caliph that I've seen before include "Title of rulers of the Islamic world" , "Historical Muslim ruler" , "Islamic leader" , "Harun al-Rashid, say" , "Chief Muslim ruler" .)