The portraits of the governors are defined in the main Governors database table. There are three columns that relate to the visuals: Image, PortraitImage and PortraitImageSelected.
The one referenced in the Image column is 178x242 pixels and has the colour background. I don't 100% know which parts of the game's UI this one is used in, but a reference example can be found under: \Sid Meier's Civilization VI SDK Assets\Civ6\DLC\Shared\pantry\Textures\GOVERNOR_CITY_DEFENDER.dds.
The one referenced in the PortraitImage column is 206x208 pixels. I believe this is used in the main governors panel. A reference example can be found under: \Sid Meier's Civilization VI SDK Assets\Civ6\DLC\Shared\pantry\Textures\GovernorNormal_Defender.dds.
Finally, the one referenced in the PortraitImageSelected column is 326x339 pixels. I believe this is used when you are looking at a single governor, in detail (including the full tree of their promotions. A reference example can be found under: \Sid Meier's Civilization VI SDK Assets\Civ6\DLC\Shared\pantry\Textures\GovernorSelected_Defender.dds.
You'll need each of your three images to be registered/added to an XLP of the UITexture class (similar to other icons/images). Then the XLP name is used as the entry in the three columns in the Governors table.
In addition to this, there are actually a number of icons used. There is a 32x32 and 64x64 pixel icon of the governor image. There are 32x32 and 22x22 pixel Fill and Slot icons. And there is a 24x24 pixel governor promotions icon. You can find all but the last one defined in the \Sid Meier's Civilization VI\DLC\Expansion1\Data\Expansion1_Governors.xml file - they follow a very similar principle to all other icons.
The final one (the governor promotions icon) is defined in \Sid Meier's Civilization VI\DLC\Expansion1\Data\Expansion1_Icons_GovernorPromotions.xml - again, it follows an identical principle to all other icons.
Of course, in your own mod you'll be replacing the definitions for the relevant Governor, in all cases, to replace all of the appropriate imagery. Hope that helps.