Having had a lot of drinks, started to smoke (3,2)
I believe the answer is:
lit up
'started to smoke' is the definition.
(I've seen this in another clue)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for lit up that I've seen before include "like a bulb, perhaps?" , "Drunk (as a bulb?)" , "was illuminating" , "Drunk (informal)" , "bulb so transformed room?" .)