Clue: Major cut to obsolete weapon, with political co-operation (10)
Answer: BIPARTISAN
Explanation: Definition: with political co-operation
BI[g] + PARTISAN , as carried by the yeomen of the Guard. Chambers calls it "a halberd-like weapon with twin axe-blades or spikes", and says the name is "of doubtful origin", so presumably not related to the more meaning of "partisan"