Hi User , Thanks for reaching out to MS Q&A
I think you are not able to enable the private link not because of create long ago but maybe because you may have selected Private access (vnet integration) option as networking option for your server
As when you create an Azure Database for PostgreSQL flexible server instance, you must choose one of the following networking options: Private access (VNet integration) or Public access (allowed IP addresses) and Private Endpoint
So can you please check which option you are using and if it is Private access (vnet integration) you cannot change to Public access (allowed IP addresses) and Private Endpoint as once you create an Azure Database for PostgreSQL flexible server, you cannot change the networking option. If you select Public access (allowed IP addresses) when you create the server, you cannot change to Private access (VNet Integration) after the server is created. Similarly, if you select Private access (VNet Integration) when you create the server, you cannot change to Public access (allowed IP addresses) after the server is created. It is recommended to create your server with private access to help secure access to your server via VNet Integration.
Please check these links for more info ->
Kindly accept answer if it helps, Thanks!