Old Bet's touch of grey heralds advancing years (4)
I believe the answer is:
gage
'old bet's touch' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'grey heralds advancing years' is the wordplay.
'grey heralds' becomes 'g' (I can't explain this - if you can you should believe this answer much more).
'advancing years' becomes 'age' (a person's age).
'g'+'age'='GAGE'
'of' is the link.
Can you help me to learn more?
(Other definitions for gage that I've seen before include "Glove thrown down by knight as challenge" , "Pledge" .)