They're proverbially old, and sick at heart (5)
I believe the answer is:
hills
'they're proverbially' is the definition.
The definition suggests an adverb but the answer is not.
'old and sick at heart' is the wordplay.
'old' becomes 's' (I can't explain this - if you can you should give a lot more credence to this answer).
'and' is a charade indicator (letters next to each other).
'sick' becomes 'ill' (synonyms).
'at' means one lot of letters go next to another (I've seen this in other clues).
'heart' becomes 'h' (card game abbreviation).
's' after 'ill' is 'ills'.
'ills' after 'h' is 'HILLS'.
Can you help me to learn more?
(Other definitions for hills that I've seen before include "Elevations of land" , "Heights; tors" , "High terrain" , "Mounts" , "See 7" .)