Yes, you have a few options for this:

  1. You can link a button or text in the app to your existing payment gateway - take payment, then manually add your client/user to the product. 
  2. If your current payment processor offers a Zapier integration, you could set up a trigger from your payment processor that fires when theres a successful sale, then an action in Movement that creates an account in your app for the client who purchased a product through this payment processor, and gives the new account access to a product.