Am I entitled to a lower price if the provider offers new customers a lower price for the service?

The main rule is that the agreed price applies. Therefore, you cannot demand to receive a price reduction during the binding period unless otherwise stated in the agreement. If your operator offers a lower price to new customers than what you are paying, the operator is not obliged to lower your price unless there is a “lowest price guarantee” or similar in the agreement. However, you can contact the operator if you have an open-ended contract and see if you can get a better offer.