Taper lit up, designed primarily for small explosive (6)
I believe the answer is:
petard
'small explosive' is the definition.
'taper lit up designed primarily' is the wordplay.
'lit up' indicates an anagram (lit up can mean drunk).
'primarily' says to take the initial letters.
The initial letter of 'designed' is 'd'.
'taper' anagrammed gives 'petar'.
'petar'+'d'='PETARD'
'for' acts as a link.
(Other definitions for petard that I've seen before include "Explosive device carried to blow in a door" , "A small bomb - don't be hoist by your own" , "Explosive device, one could have been hoist by their own, of old" , "Small bomb; one to be hoist with" , "Possession that one may be hoist with" .)