Axe having a second-rate shine, needing head scrubbed (7)
I believe the answer is:
abolish
'axe' is the definition.
(I've seen this before)
'a second-rate shine needing head scrubbed' is the wordplay.
'second rate' becomes 'b'.
'shine' becomes 'polish' (synonyms).
'needing head scrubbed' means to remove the first letter.
'polish' with its first letter removed is 'olish'.
'a'+'b'+'olish'='ABOLISH'
'having' is the link.
(Other definitions for abolish that I've seen before include "Put an end to, as with slavery" , "Annul - expunge" , "Put an end to, a rule perhaps" , "Cancel, annul" , "Get rid of" .)