Elderly to a rising degree! (4)
I believe the answer is:
aged
'elderly' is the definition.
(synonyms)
'rising degree' is the wordplay.
'rising' becomes 'age' (I can't explain this - if you can you should believe this answer much more).
'degree' becomes 'd' (abbreviation for the degree in measuring angles).
'age'+'d'='AGED'
'to a' acts as a link.
Can you help me to learn more?
(Other definitions for aged that I've seen before include "Ripened, matured" , "way over the hill" , "Long in the tooth" , "not a modern copy" , "Time-worn" .)