deferment
An official permission to delay something until later.
A deferment is an official postponement or delay of something you're supposed to do, usually granted for a legitimate reason. When a student gets a deferment on their college admission, they're allowed to start a year later than planned, perhaps to travel or deal with a family situation. When someone receives a deferment on a loan payment, the bank agrees to let them wait before they have to start paying it back.
The key difference between a deferment and just putting something off is that a deferment is official and approved. You can't simply defer your responsibilities whenever you feel like it: someone with authority has to agree that your reason for postponing makes sense. During times of war, young men have sometimes received draft deferments, meaning the government allowed them to delay or avoid military service for reasons like college enrollment or essential work.
The verb form is defer. When you defer something, you're pushing it to a later time with permission. Notice that this is different from canceling: a deferment means you'll still have to do the thing eventually, just not right now. If a judge grants a deferment of someone's prison sentence, that person still has to serve the time, but later rather than immediately.