The card "British Colonial Disputes" says "one British Army" cannot advance, but you place an "Inactive Leader" marker on it.
If that army's leader gets reassigned to some other army, I suppose that the rules mean what they literally say:
Go with the literal interpretation as far as you can.
E.g. A leader is on Champlain, which gets marked "inactive". Another card causes that leader to be moved to St Lawrence. St Lawrence will advance and Champlain will (still) not advance, right?
That sounds like the literal interpretation.
And just to confirm: "ensuing" means "next", which might be in the following turn, if the British Colonial Disputes were drawn by a French leader's special ability or some French action, right?
Yes, that sounds right.