Pet jumps up to grab a stick (4)
I believe the answer is:
goad
'stick' is the definition.
(a goad is a stick for prodding cattle)
'pet jumps up to grab a' is the wordplay.
'pet' becomes 'dog'.
'jumps up' says the letters should be written backwards (I've seen 'jumping up' mean this (in a down clue, letters go up)).
'to grab' means one lot of letters goes inside another.
'dog' in reverse letter order is 'god'.
'god' enclosing 'a' is 'GOAD'.
(Other definitions for goad that I've seen before include "Arouse" , "'Prod, urge (4)'" , "A dog to urge on" , "Prod with a pointed stick" , "Provoke, spur" .)