It applies immediately.
If you change unit type, then you'll get low morale right during the battle. The same goes with acquiring and losing tactic, combat ability and discipline bonuses. It doesn't matter what's the source - advisers, policies, new tech, ideas.
One exception - morale bonus. It only increases max morale, and you need some time to replenish it.
P.S. I don't have a proof link, but I have fist-hand experience with it. I tested it thoroughly with Common Sense 1.12.1, and I continue to observe this during recent campaigns, the latest being 1.16