Doctor clings to a longing for the past (9)
I believe the answer is:
nostalgic
'longing for the past' is the definition.
(I've seen this before)
'doctor clings to a' is the wordplay.
'doctor' indicates an anagram.
'clings'+'to'+'a'='clingstoa'
'clingstoa' anagrammed gives 'NOSTALGIC'.
(Other definitions for nostalgic that I've seen before include "Fondly remembering the past" , "Sentimental about the past" , "Wistful" , "Looking backwards" , "Longing for something past -- at closing (anag)" .)