The requirement that colonists pay for the upkeep of british soldiers is called

The requirement of colonists to pay for the upkeep of British soldiers is known as Quartering. This requirement was part of the Quartering Act and was an amendment to the Mutiny Act.

The answer is: QUARTERING ACT.

Explanation:

With the Quartering Act the British Parliament required the governments of the American colonies to give the British soldiers house and food. The Quartering Acts required annual renewal by Parliament. It was in first place intended to solve issues that arose during the French and Indian War. Later, it caused tension between the Colonies and the English. These tensions probably led to the American Revolution.