"Have got to" is used to express necessity and obligation.
Examples:
Most modal verbs behave quite irregularly in the past and the future. Study the chart below to learn how "have got to" behaves in different contexts.
2. SHIFT TO "HAVE TO" You had to be on time if you wanted to get a seat in the crowded theater.
3. You have got to be there on time tonight if you want to get a seat in the crowded theater.
2. SHIFT TO "HAVE TO" You didn't have to be there on time to get a seat.
3. SHIFT TO "HAVE TO" You won't have to be there on time to get a seat.
Haven't you got to finish that project today?
"Haven't got to" is primarily used to ask about future obligations. It can be used in statements, but this is less common.