Doze off during it? Not appropriate (5)
I believe the answer is:
inapt
'not appropriate' is the definition.
(I've seen this before)
'doze off during it?' is the wordplay.
'doze off' becomes 'nap'.
'during' indicates putting letters inside.
'nap' inserted within 'it' is 'INAPT'.
(Other definitions for inapt that I've seen before include "Inappropriate" , "badly judged" , "It's clumsy" , "Unsuitable - paint (anag)" , "not seemly" .)