Doesn't have many a sound axe (5)
I believe the answer is:
lacks
'doesn't have' is the definition.
(lacking something means not having it)
'many a sound axe' is the wordplay.
'many' becomes 'l'.
'sound axe' becomes 'cks' (I can't justify this - if you can you should give a lot more credence to this answer).
'l'+'a'+'cks'='LACKS'
Can you help me to learn more?
(Other definitions for lacks that I've seen before include "Needs" , "Has a want" , "Doesn't have" , "Wants, is deficient in" , "Is without, wants" .)