When you use chlorine tablets in your pool you should never place any chlorine tablets in your pools skimmer as it can cause damage.
You can install a chlorinator that will work with your existing pool pump which can help keep the pool water properly chlorinated.
You can also buy a floating chlorinator which is just a plastic vessel that holds chlorine tablets that will release the chlorine in the pool water when needed.
But never place any chlorine tablets in your pool skimmer because it could lead to problems and damage.