Pavlo’s approach
First, I would discuss with the another team if it's possible to break down the implementation by some meaningful parts which can be delivered gradually. If not and that's a strict delay, then I would inform all the stakeholders about the delay. Then I would work with marketing team who is responsible to present the feature to the final users, so they can adjust their plans accordingly. And finally I would discuss the workload for the team who was preparing the release, so they will start working on other things during the delay.