He deserted from the regiment on Tuesday (3)
I believe the answer is:
rat
'he deserted from' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'regiment on tuesday' is the wordplay.
'regiment' becomes 'RA' (Royal Artillery).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'tuesday' becomes 't'.
'ra'+'t'='RAT'
'the' is the link.
Can you help me to learn more?
(Other definitions for rat that I've seen before include "Betray like a rodent" , "Long-tailed rodent" , "Rodent pest" , "Plague-carrying rodent" , "person doing shopping" .)