I just added an additional Internal switch via Hyper-V "Virtual Switch Manager" and gave it a name of "Static Switch". Then changed it's settings via Control Panel->Network and Internet->Network and Sharing Center->Change adapter settings. Right click on the new adapter and select Properties->Internet Protocol Version 4 (TCP/IPv4) and set a static IP that is not currently used on your network, for example IP address: 192.168.199.1 Subnet mask: 255.255.255.0. No other settings are required. Click Ok and close all the parent windows.

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Add the new nic to the Hyper-V machine via the settings for the VM, Add Hardware->Network Adapter-Add. Select the 'Static Switch' and click OK.

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Edit your client virtual machine network settings, in my case Ubuntu 20.10 so it's Wired Settings for eth1 (the new 'Wired Connection'). I disabled IPv6 and edited the IPv4 settings using a manual configuration (static IP) setting the IP address to 192.168.199.2 and a net mask of 255.255.255.0 and a gateway of 192.168.199.1 (The 'Static Switch'). No other settings are required. Click Apply and check that the network eth1 is connected.

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You should be able to ping 192.168.199.1 from the client VM and ping 192.168.199.2 from the host machine.

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This configuration will persist after a reboot and you can edit your hosts file on the host machine with whatever name you want, eg 192.168.199.2 my.vm.machine

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Note: You will need to edit the hosts file as an administrator.