Battle against last in third division (4)
I believe the answer is:
ward
'division' is the definition.
(I have seen 'Division of borough ' mean 'ward' so perhaps 'division' could also mean 'ward')
'battle against last in third' is the wordplay.
'battle' becomes 'war' (I've seen this before).
'against' says to put letters next to each other.
'last in' indicates one should take the final letters.
The last letter of 'third' is 'd'.
'war'+'d'='WARD'
(Other definitions for ward that I've seen before include "number of patients" , "Separate room" , "One under the protection of another" , "Doctor in 5A 1D [PROFUMO AFFAIR]" , "Hospital unit" .)