Cut or share, possibly (5)
I believe the answer is:
shear
'cut' is the definition.
(I know that shear is a more specific form of the action shave)
'share possibly' is the wordplay.
'possibly' indicates anagramming the letters.
'share' anagrammed gives 'SHEAR'.
'or' acts as a link.
(Other definitions for shear that I've seen before include "Cut the wool of 14 across" , "strain" , "Cutter" , "Cut sheep's woll with large scissors" , "Cut wool off (a sheep)" .)