Alec's reviewed schedule about moving staircase (9)
I believe the answer is:
escalator
'moving staircase' is the definition.
('escalator' can be a synonym of 'moving staircase')
'alec's reviewed schedule about' is the wordplay.
'reviewed' indicates an anagram (To look at again and re view).
'schedule' becomes 'rota' (I've seen this before).
'about' says the letters should be written in reverse.
'rota' reversed gives 'ator'.
'alecs' with letters rearranged gives 'escal'.
'escal'+'ator'='ESCALATOR'
(Other definitions for escalator that I've seen before include "effortless steps" , "it moves up and down" , "nonstop flight" , "Carol eats (anag.)" , "Moving stairs" .)