Finish special edition medicated (5)
I believe the answer is:
dosed
'medicated' is the definition.
(dosing is a kind of medicating)
'finish special edition' is the wordplay.
'finish' becomes 'do'.
'special' becomes 'S' (common abbreviation as in Special Air Service).
'edition' becomes 'ed' (abbreviation).
'do'+'s'+'ed'='DOSED'
(Other definitions for dosed that I've seen before include "Administered a portion of medicine to" , "Medicated" , "Given a drug" , "Treated with medicine" , "Gave medicine to" .)