The legal relation that arises when one person delivers possession of personal property to another under an express or implied agreement to return the property at a later date is called a:

BAILMENT

Explanation:

Bailment is a legal relationship where physical possession but not ownership of personal property is been transferred from one person to another .

Bailment also means the delivery of goods or property of a person to another person to whom permission is given to have the goods and the person is under an obligation to take reasonable care of the property placed under its possession or care.