Mum or Dad could peel nutshells (6)
I believe the answer is:
parent
'mum or dad' is the definition.
(I've seen this before)
'peel nutshells' is the wordplay.
'peel' becomes 'pare' (synonyms).
'nutshells' becomes 'nt' (I am not sure about this - if you are sure you should believe this answer much more).
'pare'+'nt'='PARENT'
'could' acts as a link.
Can you help me to learn more?
(Other definitions for parent that I've seen before include "Procreator" , "The company of which others are subsidiaries" , "E.g. father" , "Uncle's sibling?" , "One with children" .)