Last to move, grabbing red bag (7)
I believe the answer is:
satchel
'bag' is the definition.
(satchel is a type of bag)
'last to move grabbing red' is the wordplay.
'to move' indicates an anagram.
'grabbing' is an insertion indicator.
'red' becomes 'Che' (as in Che Guevara, a communist or 'red').
'last' with letters rearranged gives 'satl'.
'satl' placed around 'che' is 'SATCHEL'.
(Other definitions for satchel that I've seen before include "Small case with a shoulder strap" , "Get school item" , "Shoulder bag as for schoolbooks" , "Schoolchild's carrier" , "Bag with a flap and strap" .)