Hi , There are various ways to lower nitrate in your tank , all of which need a reasonable amount of research as there are pros and cons to all , here is an article all about nitrate in the aquarium it's effects and various ways to deal with it ,

Aquarium Chemistry: Nitrate in the Reef Aquarium — Advanced Aquarist | Aquarist Magazine and Blog

A Water change will also help reduce levels instantly and will give you a little time to decide what way you'd like to go .

It's likely the last person wasn't maintaining the tank too well, but moving the rocks, stirring up sand, etc. will all add to die off and increased nitrates.  No ammonia or nitrite is a good sign though, and shows there is a lot of bacteria present to deal with the die off.

As said, a big water change will be the fastest, easiest way to get them down, and give you a good starting point. 

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