Unless you QT every single thing that ever goes into your tank EVER (corals, inverts, fish, rock, you name it ) its very likely you'll have ich unless you're running a UV sterlizer and ozone. With a sterilizer there can be some trade offs in a reef tank (I don't have personal experience but I hear it isn't good for your copepod population so if you ever wanted to have a mandarin you would have to be careful of the size of tank, rock etc)
That said, if you do plan on doing as such, you'll need to remove all fish and leave your tank fallow for 6-8 weeks I believe is the magic number. I'd go with 8 to be sure. This is to rid the parasite that may not have found a host and is waiting around in a tank. Without a host to feed on it should die off.
If you don't plan on dedicated QT, don't fret. With strong healthy fish ich usually goes dormant and doesn't bother anyone after a flare up. Without stressors in the tank (temperature swings, bad parameters, fighting, agrression, territory issues) it can remain dormant and not harm your fish. You may not see a breakout for months or even years until a fish is weakened perhaps by old age, an accidental injury, etc and even then it may or may not succumb.
Ich is out there in the wild, on many fish that come in and the goal in the home aquarium is to do the best we can to simulate that natural environment.
Cleaner gobies/shrimp can help with the external parasites. Adding garlic to the food should help boost the immune system and allow a fish to stave off ich.
There are very few actual "cures" for it - one of which is copper which you'd need to use in a seperate QT tank, the other is hyposalinity treatments which should also be done in a separate tank with ALL fish for both methods since you already have your LR and what not cycled and setup in your tank.
I wouldn't panic yet- you just added the angel and it may take a few days to figure out its territory and in the meantime if all fish are healthy and not stressed it should fade away on its own.
Best of luck with whatever method you decide to go with!