Clergyman losing head with American or Greek flier (6)
I believe the answer is:
icarus
'greek flier' is the definition.
'icarus' can be an answer for 'flier' (I have seen 'Foolhardy flier ' mean 'icarus' so perhaps 'flier' could also mean 'icarus'). I am not sure about the 'greek' bit.
'clergyman losing head with american' is the wordplay.
'clergyman' becomes 'vicar' (vicar is a kind of clergyman).
'losing head' means to remove the first letter.
'with american' becomes 'us' (abbreviation for United States. I am not sure about the 'with' bit.).
'vicar' with its first letter removed is 'icar'.
'icar'+'us'='ICARUS'
'or' is the link.
Can you help me to learn more?
(Other definitions for icarus that I've seen before include "Son of Daedalus whose wings melted fatally" , "he drowned" , "Ill-fated son of Daedalus" , "One whose wings melted" , "Daedalus's son" .)