Airline supported by Church composer (4)
I believe the answer is:
bach
'composer' is the definition.
(Johann Sebastian Bach)
'airline supported by church' is the wordplay.
'airline' becomes 'BA' (British Airways).
'supported by' means one lot of letters go next to another (in a down clue, some letters hold up others).
'church' becomes 'ch' (common abbreviation).
'ba'+'ch'='BACH'
(Other definitions for bach that I've seen before include "Brandenburg Concertos composer, d. 1750" , "German composer, who had twenty children, d.1750" , "Family of German composers" , "J. S. --, baroque composer" , "German composer (affectionate to a Welshman?)" .)