Assuming you are using Scrum, if the story is too much to do in a single sprint then it should be split into new stories (not "tasks") each with their own estimate and acceptance criteria. In that case the original story is no longer needed but the new stories might be labelled or grouped together as an "epic" that spans more than one sprint. Epics don't need estimates of their own as they are simply done whenever there are no more associated stories to complete.
Within a single sprint it is common to break down each story into tasks but this should normally be done for the sprint backlog only; that is, after the story has already been accepted for the sprint and the team has agreed that it is achievable within the sprint. That being so, it's not usually necessary for the Product Owner or other stakeholders to see estimates for individual tasks because the sprint goal is already defined and agreed.
If your team do find it helpful to estimate tasks within a sprint then I suggest you leave the estimate for the story unchanged. I would recommend that in the interests of transparency and simplicity you adopt a policy that a partially complete story does not count towards the sprint velocity at the end of the sprint. Only a completed story counts and in that case the original story estimate is what matters. Measure sprint velocity based on the estimate you agreed before or during sprint planning rather than based on any estimates the team assigned to individual tasks.