[Update]: Blizzard has now made it significantly easier to acquire Rank 3 Essences, and it's thankfully not even all that grindy.
While Blizzard has slowly but surely made leveling in Battle for Azeroth a faster and more pleasant affair, getting your alternate characters ready for the end-game is still needlessly tedious. You not only have to go through the usual process of collecting gear and Azerite Power, but you also have to unlock and level Azerite Essences all over again, some of which require you to invest a considerable amount of time into PvP or nearly obsolete content.
Thankfully, it seems that Blizzard will soon be addressing this problem and making alts a lot more attractive to veteran players. Basically, once you've unlocked a Rank 3 Essence on one character, you'll be able to also unlock it for your other characters by completing everything from Horrific Visions to Mythic Keystone Dungeons and PvP matches.
Each of these will award you a brand new currency, Echoes of Ny'alotha, which you can then exchange with MOTHER in the Heart Chamber for any eligible Rank 3 Essence. The exact number of Echoes needed for each Essence, as well as the amount that will drop per activity, is still unknown. However, since the Echoes drop from content you'll need to do in order to gear up your character anyway, it should feel significantly more natural than the current iteration.
You can read a little bit more about these upcoming changes, as well as follow any further updates, over at the official website.