There are several solutions you can choose from in case you want to use a payment service provider that is not yet connected with Online store.
If the gateway you want to use supports Authorize.Net SIM emulation, you can set it up in your store following this guide: Using gateways that can emulate Authorize.Net SIM.
If you are not sure, whether the payment gateway of your choice can emulate Authorize.Net, please check it with the Customer Support of the payment provider.
You can connect your store to the necessary payment gateway by building a custom integration with the help of Payment API. You can develop the solution yourself or hire someone.