Churchman heading off with American high-flier (6)
I believe the answer is:
icarus
'high-flier' is the definition.
(I've seen this before)
'churchman heading off with american' is the wordplay.
I cannot quite understand how this works, but
'american' could be 'us' (abbreviation for United States) and 'us' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for icarus that I've seen before include "Excessively high flier" , "Son of Daedalus, who flew too close to the sun" , "Ancient Greek who flew too close to the sun" , "One whose wings melted" , "Ill-fated flier of myth" .)