Quickly walk after adult (5)
I believe the answer is:
apace
'quickly' is the definition.
('apace' can be a synonym of 'quickly')
'walk after adult' is the wordplay.
'walk' becomes 'pace' (pacing is a kind of walking**).
'after' says to put letters next to each other.
'adult' becomes 'a'.
'pace' put after 'a' is 'APACE'.
(Other definitions for apace that I've seen before include "fast" , "(Move on) swiftly" , "Quick" , "flat out" , "At a rapid rate" .)