There were quite a few black people in Europe following the fall of the Roman Empire and growing trade with Africa in the 15th and 16th centuries. A few black Tudors are recorded in the courts of Henry VII, Henry VIII, Elizabeth I, and James I, and Queen Charlotte, wife of George III (the Mad King), was black.

The technology and fashion in Game of Thrones is consistent with that of the late medieval period (1500s-1600s). While HotD occurs 200 years earlier based on the in-universe timelines, the weapons, armor, and styles are still consistent with that later period, so I think it's fair to say the Game of Thrones universe is essentially based on an extended late medieval period, rather than HotD occurring in the late 14th century and GoT in the 16th century.

So, it would be consistent with the time period for there to be black people in the court.