Your nitrates will not drop without a water change (in this case). However, high nitrITES can cause a false high nitrATE reading, so once your biological filter is efficiently processing nitrite to nitrate you should see 0 nitrite and a true nitrate level. This may be 5, it may be 50. A water change is recommended at this point and the size of the WC can depend on the amount you want to lower your nitrates.
But... since nitrites don't harm saltwater fish the way they do freshwater fish, most experienced reefers don't even test for nitrites. If you add an ammonia source (fish food, etc) and in 24 hours you have no ammonia (and some nitrates, which you already have), then the tank has a biological filter that can safely process a small bioload.
Add livestock slowly in order for the biological filter to catch up to the new bioload...