What comes after a flight is a pause between flights (7)
I believe the answer is:
landing
This clue is a double definition.
'what comes after a flight' is the first definition.
(eg a plane landing)
'a pause between flights' is the second definition.
(area between flights of stairs)
'is' is the link.
(Other definitions for landing that I've seen before include "Level area between stair flights" , "A gap between flights" , "getting in fish" , "Top of a staircase" , "Alighting point" .)