Cold comfort before illness finally stops (6)
I believe the answer is:
ceases
'stops' is the definition.
('cease' can be a synonym of 'stop')
'cold comfort before illness finally' is the wordplay.
'cold' becomes 'c' (eg on taps).
'comfort' becomes 'ease' (easing is a kind of comforting).
'before' says to put letters next to each other.
'finally' suggests the final letters.
The last letter of 'illness' is 's'.
'c'+'ease'+'s'='CEASES'
(Other definitions for ceases that I've seen before include "Finishes" , "Comes to an end" , "Stops or discontinues" , "stops working" , "Discontinues, ends" .)