Demanding to have top lowered, is obliged (5)
I believe the answer is:
ought
'is obliged' is the definition.
(you ought to do something you're obliged to do)
I can't explain the remainder of the clue.
(Other definitions for ought that I've seen before include "Be logically necessary" , "Tough (anag)" , "Have/has a duty (to do)" , "Be bound" , "Has a duty (to do something)" .)