Part of airport entered by a person taking flight (7)
I believe the answer is:
runaway
'person taking flight' is the definition.
(someone running away)
'part of airport entered by a' is the wordplay.
'part of airport' becomes 'runway'.
'entered by' indicates putting letters inside (I've seen this in other clues).
'runway' enclosing 'a' is 'RUNAWAY'.
(Other definitions for runaway that I've seen before include "such a success?" , "refugee?" , "Absconder" , "desert" , "Fugitive" .)