Drunk later today? That's not on (5)
I believe the answer is:
tight
'drunk' is the definition.
(slang term)
'later today? that's not on' is the wordplay.
'later today?' becomes 'tonight' (I've seen this before).
'that's not' indicates named letters should be taken away (that has not).
'tonight' with 'on' taken away is 'TIGHT'.
(Other definitions for tight that I've seen before include "Drunk - a near thing!" , "Closely constrained, constricted" , "South American nation" , "It's not enough" , "Hard to undo or open" .)