Tool given push, then left (6)
I believe the answer is:
shovel
'tool' is the definition.
(shovel is a kind of tool)
'push then left' is the wordplay.
'push' becomes 'shove' (shove is a kind of push**).
'then' means one lot of letters go next to another.
'left' becomes 'l' (common abbreviation).
'shove'+'l'='SHOVEL'
'given' is the link.
(Other definitions for shovel that I've seen before include "Digging implement" , "Spade-like scoop" , "Spade with a broad blade" , "Tool like a spade" , "Tool for moving, eg, coal" .)