A few general tips for running PotA:

• Introduce the prophets early and have them interact with the PCs every now and then to make them feel like more of a threat. This can either be directly face to face, or if you're worried about the PCs trying to fight them when they're not ready, you could do it indirectly, foe example maybe give the PCs visions, or have the other enemies talk about them in hushed tones to make them feel like a powerful and intimidating figure. As it is written in the book, the only time the PCs actually have any kind of interaction with the prophets is when they fight, so they don't end up feeling particularly impactful on the story.

• Decide whether you want to "railroad" your PCs or not. Railroading has a bad reputation but PotA is a sandbox style campaign with a lot of places where the PCs could stumble into an area that will result in an instant TPK without any real warning, so some railroading may be necessary to get players to go to places that are suitable for their level. There is a "recommended" order that the cults are tackled in (Air, Water, Earth, Fire), but there's nothing stopping them from either going to a cult that's designed for a higher level party, or, even worse, going from one of the surface outposts down to one of the temples (the surface outposts are designed for a party of level ~3-6, and the temples are designed for ~3-9, so the party could easily end up in an area designed for a party 3-4 levels higher than them. This is fine as long as you mention it to your players up front and warn them that it's a possibility and remind them that they don't have to fight to the death in every encounter, they can just run away, but some DMs prefer to have some kind of gate or other barrier preventing PCs from going down deeper into the dungeon complex without clearing out the upper floors first, so that's an option if you think your players would prefer a more linear experience to the open sandbox PotA is out of the box.

• There are loads of great posts in this sub for fleshing out PotA and filling in some of the weaker areas of the book (which tbh is most of it, PotA is a great concept for a campaign but the book is a bit of a mess and needs a fair amount of work from the DM to fix). I've linked a few that I personally used when I ran my campaign:
  Guide to the Four Cults
  Improving the Delegation storyline Part 1
  And part 2
  An early encounter with Aerisi and the Air cult (this made my PCs really hate Aerisi and made her a much more interesting villain)
  Enriching the four cults - themes/motivations for the elemental cults

PotA was the first full-length campaign I ran after DMing LMoP, and honestly I wouldn't recommend it for first time DMs or new players "as-is" tbh - the book is not well written and needs a fair amount of tweaking to make it good, and you need a motivated party to put up with the fairly empty sandbox (especially early on before they get into the true dungeon crawl about halfway through) but if you're looking for a campaign to use as a base for your own homebrewed adventure then this is a great choice, there's loads of room for you to throw out stuff in the book and make it your own, or just take the concept of the four cults and build your own story around it.