Locate your desired character image. You're on the internet, so that should be straightforward. You'll ultimately need two copies of different sizes.

Crop, resize and rename. Use an image resizer to make one portrait image of 210x330 pixels and one of 79x96 pixels. The larger one should be called mycat_lg.png (or whatever_lg.png) and the smaller one needs to be named mycat_sm.png. Those _lg and _sm suffixes are crucial, and the forename part (mycat) should obviously be the same for each.

Bung them in the right folder. Find the SteamLibrarysteamappscommonTyrannyTyranny_Datadataartguiportraitsplayermale (or female) folder string on your PC. Pop both images into male or female as desired.

Load up the character creation screen and (hopefully) revel in your genius as the portrait appears in-game.