Plague hunter possibly gets two-hour shift (3,5)
I believe the answer is:
dog watch
'two-hour shift' is the definition.
(naval term for a shift keeping watch)
'plague hunter possibly' is the wordplay.
'plague' becomes 'dog' (both can mean to follow or repeatedly torment).
'hunter possibly' becomes 'watch' (hunter is a kind of watch).
'dog'+'watch'='DOG-WATCH'
'gets' is the link.
(Other definitions for dog watch that I've seen before include "Crufts?" , "The afternoon shift" , "two-hour shift" .)