Very old have nurse to push forward (6)
I believe the answer is:
hasten
'push forward' is the definition.
(thesaurus)
'very old have nurse' is the wordplay.
'very old have' becomes 'hast' (archaic form of the word 'have').
'nurse' becomes 'en' (abbreviation for enrolled nurse).
'hast'+'en'='HASTEN'
'to' acts as a link.
(Other definitions for hasten that I've seen before include "Move quickly" , "Step up" , "race? - with 26a" , "dash" , "Travel with expedition" .)