Payment Gateway how to redirect customer to PSP page after retreiving URL in Gateway Client response

I’m developing a custom payment gateway but hit a wall trying to redirect the customer to the 3th party page.
I’ve setup the gateway such that the Client (Gateway/Client/Client.php) sends the request to the PSP correctly. The response from the PSP includes a redirectUrl, which the customer has to visit in order to complete the payment.

I’ve looked at lots of code examples from the Paypal Express extension but can’t figure out how it should work in this case.
I did get it working to provide an arbitrary URL from the ConfigProvider to the front-end, but I don’t know how I can get the URL from the PSP in the ConfigProvider.

So in essence, how do I get the Client’s response (return value from placeRequest() ) to configProvider such that this can be used in the front-end store?
Or should I use another approach (and if so, which one?)

Note: I’m totally new to working with orders and payment extensions in Magento