Welcome to AA!
Nitrates can get high for many reasons.
What size tank is it and what kind of filtration do you have?
Do you have a protein skimmer?
Do you use RO/DI water for top offs and water changes?
What fish do you have, what do you feed them and how often do you feed them?
An anemone alone won't cause high nitrates. Do you try to feed it and if so, what do you use?