Desert from the artillery on Tuesday (3)
I believe the answer is:
rat
'desert' is the definition.
(abandon treacherously)
'artillery on tuesday' is the wordplay.
'artillery' becomes 'RA' (Royal Artillery).
'on' means one lot of letters go next to another.
'tuesday' becomes 't'.
'ra'+'t'='RAT'
'from the' is the link.
(Other definitions for rat that I've seen before include "Sewer rodent" , "one who deserts the sinking ship?" , "Plague-carrying rodent" , "one not going down with ship" , "one escaping doomed vessel?" .)