Hello,
What you can do is use a Azure VPN solution to communicate to on-prem services from AKS:
Using Azure kubernetes managed service in private cloud topology
https://www.cloudready.club/azure/hubspoke-topology/
You need to establish a VPN Gateway between your on-prem LAN and Azure tenant.
What is Azure VPN Gateway?
https://learn.microsoft.com/en-us/azure/vpn-gateway/vpn-gateway-about-vpngateways
"Azure VPN Gateway is a service that uses a specific type of virtual network gateway to send encrypted traffic between an Azure virtual network and on-premises locations over the public Internet. You can also use VPN Gateway to send encrypted traffic between Azure virtual networks over the Microsoft network. Multiple connections can be created to the same VPN gateway. When you create multiple connections, all VPN tunnels share the available gateway bandwidth."
If this is helpful please accept answer.