Very little information to go with here but we will see if we can narrow down the issue based on how it should work. When you start Pro, configured for Pro Named User license via Enterprise, it will display the portal login dialogue. The dialogue itself verifies Pro is able to make an https connection to the portal. The user provides an Enterprise account and password. It then makes a call to the portal. The portal verifies the account and password is valid and determines if it was assigned a Pro NU license. If it does not, it will throw an error back to Pro indicating the account was not assigned a Pro NU license and to log in with an account that does. Because you did not get this error likely means there is no communication issue up to this point. Assuming the account used to log in was assigned a Pro NU license. It send the message back to Pro indicating the Pro NU license it was assigned and a license manager server where to get the license.
Pro proceed to make a call to the license manager server through TCP/IP to retrieve the license. If it can reach the license manager and retrieve the assigned Pro license, Pro will start. If it cannot retrieve the license, it will usually display an error. In some cases, it may just close and stop. I believe this is where issue lies. Either Pro cannot find the license manager or there is there is a network issue to the license manager. Let's take a look at each.
License Manager- Go to the URL address for the poral admin. Ex. https://hostname/arcgis/portaladmin. Click on the license link. Verify the License Manager info. It it displaying the license manger as a hostname, FQDN, IP address, etc? Verify you can at least ping that name from the Pro machine.
Now that you've determined what the license manager server is, Pro must be able to communicate to the machine through two ports, 27000 and another port. You must specify these ports in the service.txt file on the license manager machine. Refer to the following link if you need more information, https://desktop.arcgis.com/en/license-manager/latest/configure-the-arcgis-license-manager-to-work-th.... Let's assume you've tied down the ports to 27000 and 27002 for example. You must open these two ports through any firewall between the two machines. From my experience, a block on one of these ports is usually the issue.
Hope that helps. Let me know how it goes.
