Country person, coarse in manner, losing head soon (7)
I believe the answer is:
lebanon
'country' is the definition.
(Lebanon is an example)
'person coarse in manner losing head soon' is the wordplay.
'person coarse in manner' becomes 'pleb'.
'losing head' means to remove the first letter.
'soon' becomes 'anon' (I've seen this before).
'pleb' with its first letter removed is 'leb'.
'leb'+'anon'='LEBANON'
(Other definitions for lebanon that I've seen before include "Country associated with cedar trees" , "Beirut's country" , "Country N. of Israel" , "Ban Noel from the country" , "E. Mediterranean nation" .)