Deserter from the artillery on Tuesday (3)
I believe the answer is:
rat
'deserter' is the definition.
(both can mean a traitor)
'artillery on tuesday' is the wordplay.
'artillery' becomes 'RA' (Royal Artillery).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'tuesday' becomes 't'.
'ra'+'t'='RAT'
'from the' acts as a link.
(Other definitions for rat that I've seen before include "Betray like a rodent" , "Renegade" , "Inform" , "One deserting sinking ship" , "Cad" .)