The most important is probably the antiquities system released with the Greymoor chapter. It has two skill lines, scrying and excavation, but can be done on any character so best to pick one with a lot of extra skill points if possible. Essentially, you find a "lead" by doing various types of content--from killing a specific boss to harvesting alchemy plants in Shadowfen--then scry on the lead with a minigame to find a dig site, where you then dig up the antiquity, or part of it, with another mingame. With the antiquities system came mythic items, which are single pieces of gear that have extremely strong stats so you'll want to get at least a couple mythics probably. It may be helpful to look up an antiquities grind guide online.

With the Summerset chapter came the Psijic skill line, which can also be situationally useful and is most often used for the Accelerate skill and its morphs. The skill line is very grindy to acquire and must be completed on the character(s) that you intend to run content with. Unlocking the skill line is pretty straight forward: do the first quest in the Summerset questline, and when you get to Artaeum, talk to the psijic quest giver there, who is separate from the main story quest giver. After that, just keep doing psijic quests.

Otherwise I can't think of many other skill lines or items that are new and super important to get. Of course there is meta gear from recent content, but you'll acquire it as you progress through the game and get back up to speed. The only other thing you might want to look into is unlocking different weapon and armor skill lines. Within the past year (I believe) it has become optimal in a few instances for magicka dps to run double daggers on the front bar instead of a staff, and it is just starting to become a choice (not yet popular but probably soon) for stamina dps to run a flame staff (the staff acquired from Maelstrom Arena* to be precise) on the backbar. And last patch and the one coming in ~3 weeks are introducing a lot of hybridization of item sets and gear, so mag dps might want to run medium armor and/or a stam set and vice versa, so you will want to gain levels in different armor passives if you haven't yet.

*Within the last year, perfected and non-perfected gear was introduced to the game, so for trials and arenas, you can now get non-perfected gear from normal mode and perfected gear from veteran mode, except for the Craglorn trials which aren't affected.