Shot by nasty piece of work over drugs (4)
I believe the answer is:
dose
'shot' is the definition.
(I've seen this in another clue)
'by nasty piece of work over drugs' is the wordplay.
'by' is a charade indicator (letters next to each other).
'nasty piece of work' becomes 'sod' (sod can mean a nasty person).
'over' says the letters should be written backwards.
'drugs' becomes 'E' (somebody 'on E' could also be 'on drugs').
'sod' reversed gives 'dos'.
'dos' next to 'e' is 'DOSE'.
(Other definitions for dose that I've seen before include "Measure (med.)" , "Measure of medicine" , "Medicinal quantity" , "some Viagra, perhaps?" , "Helping of medicine" .)