Fed up with bottom of straggly beard (4)
I believe the answer is:
defy
'beard' is the definition.
(beard can mean to face or defy)
'fed up with bottom of straggly' is the wordplay.
'up with' is an anagram indicator (letters get chucked up).
'bottom of' suggests the final letters.
The final letter of 'straggly' is 'y'.
'fed' anagrammed with 'y' gives 'DEFY'.
(Other definitions for defy that I've seen before include "Go against (authority)" , "Openly resist or refuse to obey" , "Brave" , "Disobey boldly and openly" , "Boldly resist (authority, etc)" .)