Understand hairpiece needed after time (4)
I believe the answer is:
twig
'understand' is the definition.
(I know that twig is a more specific form of the action the understand)
'hairpiece needed after time' is the wordplay.
'hairpiece' becomes 'wig' (wig is a kind of hairpiece).
'needed after' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'wig' put after 't' is 'TWIG'.
(Other definitions for twig that I've seen before include "Division of branch" , "Small shoot or branch" , "bit of wood" , "Suddenly comprehend" , "Suddenly see - bit of a tree" .)