Publicity campaign plugs gift (5)
I believe the answer is:
award
'gift' is the definition.
(award is a kind of gift)
'publicity campaign plugs' is the wordplay.
'publicity' becomes 'ad' (short for advertisement).
'campaign' becomes 'war'.
'plugs' indicates putting letters inside (plug can mean to fill a gap).
'ad' going around 'war' is 'AWARD'.
(Other definitions for award that I've seen before include "Trophy or medal, for example" , "Maybe damages" , "Bestow" , "Grant - prize" , "They are disinclined to work" .)