I've done pbp on dedicated forums before but never discord. So I'm not sure how well any of this will translate to discord. This also assumes asynchronous play, where you're not generally logged on at the same time or able to immediately reply.
I set up multiple threads to disseminate information because it's easier that way. It front-loads the work but it saves time in the long run. One thread for character creation, one for house rules, one for a setting primer, etc. There's also always one in-game thread for all the narration and PC actions. And always one thread for out-of-character chat, either about the game or general hang out and catch up. It's better to have it all down "on paper" and in one place you can point your players to. Things will get lost in the shuffle, things will be misplaced or forgotten otherwise.
Set an expected posting rate. Whatever it is, one post every 2 days, 3 days, 4 days, etc. keep it consistent. Whoever the referee is should post every time that interval passes to keep the game moving. If a player hasn't posted, they get skipped. Again, this is to keep the game moving. In pbp you can very quickly bog down into "I was waiting for X to post" and suddenly it's two weeks later and no one's posted.
The biggest bits of advice I can give are ditch initiative and minimize handling time. Both are for the same reason, they both slow the game to a crawl if not outright kill a pbp game.
Forcing players to wait to post in a particular order will kill the game dead. Either make every action simultaneous or have the referee handle initiative order. It's way easier to go with simultaneous actions.
Minimizing handling time is about reducing the number of posts required to accomplish something. In a face-to-face game having 3-5 steps to resolve an action is nothing and only takes a few seconds. In a pbp game that exact same interaction can take days for each step.
"I attack the orc. I got a 17. Does that hit?"
"Yes, that hits. What's your damage?"
"I deal 12 damage."
So anything and everything that can minimize the number of steps required (i.e. posts) to accomplish something will do wonders for your game. Announce DC up front, announce the HP and AC of monsters so the players don't have to ask, because that ask and answer can have days between them.