Plague is to lessen after time (5)
I believe the answer is:
tease
'plague' is the definition.
(I know that tease is a more specific form of bedevil)
'lessen after time' is the wordplay.
'lessen' becomes 'ease' (I've seen this in another clue).
'after' is a charade indicator (letters next to each other).
'time' becomes 't' (abbreviation).
'ease' put after 't' is 'TEASE'.
'is to' is the link.
(Other definitions for tease that I've seen before include "Kid" , "Annoy good-naturedly" , "Taunt or bait" , "Rag" , "Gently mock" .)