Yeah all the skills under Alliance War category (Assault/Support) require PVP to unlock. There are a lot of resources out there on ways to grind AP, but essentially I would try to get in a group in Cyrodiil (just post LFG in the zone), and stay near the group leader (crown icon).

Try to get kills if you can but if you are sucking at getting kills (or being one shotted all the time) then you can help with siege weapons instead (purchasable from the siege merchants). Not only do they help your team tremendously in both Defense and Offensive, but they can also wrack up some decent AP to help you rank up.

You can also spam heals if you have them, or even if you don't just put a single point into resto staff for Regeneration, just to use it as a cheap source of AP trickle.

You can also repair the keep walls after a take or defend. This way is slow and expensive gold wise, but it is another way.

Make sure you keep getting the repeatable quests from your main base for like 'Kill 20 Players', and 'Scout this place'. They will all help you grind faster. It does take a while though but the skills in those trees are totally worth it.

I have gained the most XP for the keep defense stuff so make sure you just keep an eye out for them people say one is under attack and go help defend it.

Be prepared to spend about 5-6 lengthy sessions in there to get it unlocked. It will just depend on how much action and if you are near it

Good luck!

War horn is really quick to unlock.. do the training quests in cyrodill then join a big group and just run with them for a bit... i unlocked it in about 1 hour