Way advancing years finally progress, in steps (6)
I believe the answer is:
stages
'steps' is the definition.
(both can mean parts of a process)
'way advancing years finally progress' is the wordplay.
'way' becomes 'st' (abbreviation for street).
'advancing years' becomes 'age' (a person's age).
'finally' suggests the final letters.
The last letter of 'progress' is 's'.
'st'+'age'+'s'='STAGES'
'in' acts as a link.
(Other definitions for stages that I've seen before include "Parts of a process" , "Platforms for performances" , "Puts on a play" , "Coaches" , "Phases" .)