However, it is possible to make a Westerosi faction declare war on an Essos faction if you can form a defensive pact and then get declared war upon. For Westerosi factions, diplomacy is locked and you can't form an alliance with them.

As far as I know, this is not a guaranteed method.ДЇor Essos factions, all 4 of those options should work as far as I'm aware. This will take some time and even then depend on random chance. If he doesn't want war with the faction of your choice, roll back your save and try again and again (sometimes they are willing to only go to war against 4-5 other factions but not any others). Go up to that lord, back up your save in 'Documents' and ask him for tasks to see if he wants to go to war against your desired faction (if he gives you some other task, just decline and immediately ask again). If the bartender mentions Lord XYZ is looking for someone but you better watch yourself with him, that means that lord is looking to start a war against a random faction. You can also form a defensive pact, which will force your ally to join your side if another kingdom declares war on you.Д¤) Go to the tavern of a faction and ask the bartender if 'anyone has a job for you'.

This is difficult without very good relations.ДЈ) Similarly, you can form an alliance with a faction and then declare war on another faction which will force your ally to take your side. You must provide legitimate reasons.Дў) If you have your own kingdom, form good relations with the faction and request aid against your enemy. To declare war on another faction in M&B, you generally have these 4 options:ДЎ) Become a vassal of a faction and convince your King to go to war.

Clash of kings guide