A throwback is hard to get rid of (7)
I believe the answer is:
abolish
'get rid of' is the definition.
(synonyms)
'a throwback is hard' is the wordplay.
'throwback' becomes 'bol' (I've seen this in other clues).
'hard' becomes 'h' (abbreviation used in pencil classifications).
'a'+'bol'+'is'+'h'='ABOLISH'
'to' is the link.
(Other definitions for abolish that I've seen before include "delete" , "Formally do away with" , "Put an end to (custom)" , "Put an end to, cancel" , "Drop" .)