Complete two weeklies for your alliance to increase fame in World of Warcraft Shadowlands.
Fame is how you level your Alliance, and ultimately your Soulbinds (Shadowlands version of "borrowed power"). The higher your fame level, the more features, activities and rewards you will have access to. Unlike the might of Artifacts and the Heart of Azeroth, you won't pour endless amounts of Anima into your fame. Fame is leveled in a much simpler way than either of these systems, and there is a weekly limit to how high you can climb.
There are currently (as of the date of publication) 40 Fame Ranks. Each week, your Covenant will have two weekly quests which will reward a single rank upon completion. You read that correctly: a complete ranking by quest. No Anima spill into fame until he level up, no perpetual work to keep up with everyone - just two weeklies.
Now one of those weeklies (Replenish Tank) is to farm 1000 Anima (and the Anima you have on hand before taking the quest doesn't count), but you can easily farm 400-500 per day in your Covenant's area alone. by completing world quests, looting chests (especially those marked on the map), killing rare spawns, and randomly looted quests from mobs.
The other (Rescue Lost Souls) requires you to venture into the Maw and save Tormented Souls (which will become Redeemed Souls, another endgame resource used to upgrade your Covenant's Sanctuary), but this one is arguably faster than Anima farming. So if you don't like the Maw, this week won't require the deepest of the daily dives. Simply enter, grab the souls, then release a bond (I still recommend completing your daily Maw quests, but you do).
There is a third way to earn Fame and that is by completing your Covenant's Campaign Chapters. These are unlocked by increasing your fame to the required rank, so these aren't weekly events like the first two methods. Still, once you've unlocked a new Campaign Chapter, it's worth qualifying for the Fame Rank.
Activating them will grant you one rank of fame each, and you will unlock all the rewards associated with each rank you achieve. Then you will just have to wait for the next weekly reset to level your fame again. This means you'll earn two Leaderboards per week (unless you have a Campaign Chapter unlocked, you'll get three). That said, other catch-up players will only be limited by the current cap. So your alts that are overdue (or main, assuming you missed a week or seven) will be able to complete Dungeons, World Quests, PvP, and more to earn Fame Ranks until they reach the current ceiling.
For reference, here's how the caps will increase each week:
