Part of flight from Budapest airport (5)
I believe the answer is:
stair
'part of flight' is the definition.
(I've seen this before)
'from budapest airport' is the wordplay.
'from' indicates the answer is hidden within the clue.
'STAIR' is hidden in the letters of 'budapest airport'.
(Other definitions for stair that I've seen before include "Support on which to step" , "one's seen in flight" , "something of a case" , "Rising step" , "One of a 15" .)