PLD was the defacto MT for a long time, but since they've got a lot of nice party utility skills now their role has mostly been shifted to OT. As an OT paladin you'll be responsible for stuff like:
Providing Cover (sometimes with Tempered Will) to ease damage on healers (and prevent knockback when necessary). For example in V5S the paladin will usually cover+tempered War (or Drk) MT to prevent ghost knockback a couple times in the fight. This helps your MT get uptime and increase damage. In V7S cover is used on the Prey mechanic to prevent DPS from getting hit with a nasty fire debuff. V8S uses similar mechanics again.
Additionally you'll want to use Intervention on your co-tank to ease tankbusters (and sometimes on DPS if they are taking damage you won't be able to Cover).
Other things to be aware of are the clutch Clemency. Even tho casting it will make most people's skin crawl, it's entirely possible for a run to be saved by a clutch clemency on MT or healer, or DPS, depending on the encounter. Don't focus on it but also don't forget about it. You also have a pretty nice party shield with Divine Veil. This can be stacked with other shields or you and a Warrior MT can alternate shields for various raidwide damage mechanics. Also don't forget you can alternate Reprisal with your co-tank. Alternating mitigation correctly will allow you both to stay in DPS stance more often and also help your healers get more DPS in since they won't be needing to heal for large amounts of damage.