To update the Primer client session’s billing address make a POST request to the /client-session/actions endpoint with the following body:

{
	"clientToken": clientSessionToken,
	  "actions": [
		   {
		    "type": "SET_BILLING_ADDRESS",
		    "params": {
  				"billingAddress": {
  					"firstName": firstName, // optional
  					"lastName": lastName, // optional
  		      "addressLine1": addressLine1,
  					"addressLine2": addressLine2, // optional
            "city": city,
            "postalCode": postalCode,
  					"state": state, // optional
            "countryCode": countryCode,
          }
			  }
		  }
		]
	}
}
// ⚠️ this request requires your Primer API key.
// All fields not evaluated shouldn't be sent to the BE.

please refer to the Client Session API for more details.