Grasp tip of throw rug (4)
I believe the answer is:
twig
'grasp' is the definition.
(twigging is a kind of grasping)
'tip of throw rug' is the wordplay.
'tip of' indicates taking the first letters.
'rug' becomes 'wig' ('rug' is an informal term for a wig).
The first letter of 'throw' is 't'.
't'+'wig'='TWIG'
(Other definitions for twig that I've seen before include "bit of wood" , "Suddenly comprehend" , "Suddenly see; branchlet" , "Division of branch" , "Suddenly realise" .)