What is the word for a person who rules in the place of the king or queen?

I can think of a few.

1. Regent - a regent is someone who is appointed to rule a country while the monarch is unable to do so themselves- usually it's when the monarch is a young child, or is mentally handicapped.

2. Viceroy - a viceroy is someone who is appointed to rule a colony for a monarch. The monarch is usually too far away to rule it themselves, so the Viceroy handles it for them.

3. Governor-general - very similar to a Viceroy, a governor-general usually rules an independent country that still acknowledges a monarch as their ruler. Canada and Australia, which are independent countries, each have a governor-general who rules the country in the name of the Queen of the United Kingdom.