One of the issues of Windows 7 (and Windows Server 2008 R2) is related to its inability to support 4K resolutions over RDP. Windows 7 RDP resolution is limited at 3840 x 2048, whereas 4K monitors run at 3840 x 2160, which leaves a small black strip at the top and bottom of the remote desktop window. The following article describes the way I was able to resolve this issue.
It should show that Remote Desktop Protocol 8.1 is supported:
If you’re not using Remote Desktop Protocol 8.1, first make sure that you’re running Windows 7 SP1 (latest Windows Server 2008 R2) and then go to Microsoft Windows update page at https://support.microsoft.com/en-ca/help/2923545/update-for-rdp-8-1-is-available-for-windows-7-sp1 and update your RDP to version 8.1.
Once you’re using RDP 8.1, navigate to the following page: https://support.microsoft.com/en-us/help/2989007/update-to-support-ultra-hd-resolution-for-rdp-sessions-in-windows-7-an and download Hotfix update that enables support for Ultra HD resolution for RDP sessions in Windows 7 (and Windows Server 2008 R2).
You’ll need to fill your email and Microsoft will send you a link to download, the hotfix request screen will look something like this:
Once you receive a file, unzip it and you’ll end up with a file called: Windows6.1-KB2989007-x64.msu (or something similar for Windows 2008).
Simply install it, reboot your computer and next time you RDP to Windows 7 (or Windows Server 2008 R2) your screen will properly scale to support 4K (3840×2160) resolution.