Stairs offering escape? (6)
I believe the answer is:
flight
I believe this is a double definition.
'stairs' is the first definition.
(flight is a kind of stairs)
'escape?' is the second definition.
('flight' can be a synonym of 'escape')
'offering' is the link.
(Other definitions for flight that I've seen before include "Voyage of an aircraft" , "Movement through the air" , "Trip by air" , "Group of birds - running away" , "the vanquished may take?" .)