The use of "have got" adds emphasis. "Have got" is not in the past. It is present or future tense. If you want past, you have got to use had. (Had got sounds icky. Americans use had gotten, although that modifies things a bit.) In the sense of "possession", it follows the form of has. Present: Have I got news for you! "Have got" is valid English. (Note how this is a lot more emphatic than "Have I news for you!") In the sense of "must", "have got" can be future or future perfect: Future: You've got to be on time for the show tonight! Future perfect: English has got to be the hardest language in the world to understand! Edited to add: "Have got" is an idiom. There is little sense in idioms in any language. "Have got to" is a modal. Modals are nasty in any language. Moreover, "have got to" is an idiomatic modal.