Mike, get rid of longing for facial hair (9)
I believe the answer is:
moustache
'facial hair' is the definition.
(I've seen this before)
'mike get rid of longing' is the wordplay.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'get rid of' becomes 'oust' (I've seen this in another clue).
'longing' becomes 'ache' (longing can mean aching or pining for something).
'm'+'oust'+'ache'='MOUSTACHE'
'for' acts as a link.
(Other definitions for moustache that I've seen before include "Facial hair touches Ma" , "Food trap" , "whiskers" , "Handlebar or walrus, for example" , "legacy of Zapata?" .)