The following things offer renown (a chance) but that chance has been increased as of 9.1:
Callings (one pop every day) prio those that offer renown and do them asap
The 9.0 Worlds bosses seem to always drop renown. One up per week. Can get the renown once per week.
Raid bosses have a chance to drop renown
COmpleting a dungeon of any difficulty that you have either Qued for (LFD) or used the groupfinder for (M0 and M+) has a chance to give you 1 renown at the end.
COmpleting some storyline quests (such as Bolvar’s torghast ones, as well as some of the new ones in 9.1 such as Battle of Ardenweald) may offer renown as well. I was 39 of 9.1 realease, and the Battle of Ardenweald quest offered me 1 renown, but I did my calling (which gave me one, taking me to 40) and the Battle quest no longer offered it, indicating it is “catch up”.
Winning in any pvp setting (BGs, Arena) has a chance to grant renown.
The real question is, how would you prefer to get it? Callings and world bosses are a must, but beyond that how you get it depends on your preferences.
ALSO the weekly quests (1000 anima and SHaping Fate in Korthia) offer 1 renown each BUT they are required to “hit the cap” - catch up will only take you up to cap-2, which means you must save turning these quests in until you are two below maximum, else the catch up will not take you the rest of the way.
This week the cap is 42, which means you should exhaust your catch up renown until you hit 40, then turn in those weekly quests.
If you pop into Korthia, the anima quest is now very easy to complete…after doing all the mandatory questing in Korthia I returned to my sanctum and I turned in something like 2.9k anima. Anima drops like hot cakes in Korthia.
You’re welcome, good luck. I was a slave to renown catch up last week, so I hope their “hotfix” delivers and you find you get to 40 in relative quickness.
World bosses & LFR are a quick way to get both gear, currencies & catch-up levels so you may have to consider it in a few weeks when LFR opens.
Oh yeah and don’t expect to complete the Korthia renown quest in one day, it’s designed to last a few days & burning out clearing rares and chests won’t help in the long run.
Each assault is worth 25% on their own (2 per week) & daily quests are worth 5 or 10% iirc. Just focus on daily content & you’ll get the renown quest done easily.