Mechanical filters or chemical disinfection, such as chlorination, DO NOT remove nitrate from water.
What can be used to remove the nitrates?
Reverse osmosis, electrodialysis and ion exchange are the processes that can be used to remove nitrates.
Do nitrates eat chlorine?
Nitrates encourage growth of algae. Soon your pool will turn green and algae will start sticking to the walls of your pool. The clean up of the algae is only more hindered because the nitrate will fight the chlorine you add to the pool meaning you will have to use more chlorine than usual to get rid of the problem.