Pavlo’s approach
First - gather all the information about the new feature by scheduling meetings and other communication channels with the stakeholders:
- Why the feature should be implemented urgently?
- What's its contribution towards short and long terms goals of the product? Which product metrics does it affect?
- Who should be involved into the implementation? How much effort is needed for the implementation?
If there are obvious reasons that new feature won't bring more value than current planned work, then the PM should prepare presentation with clear explanation why current work is more important.
Normally the information gained can clarify all the doubts and be a good foundation to explain the team members why the change is needed to minimize their frustration.
Communicate the changes to the team with clear explanation of the urgency. Address all the concerns, gather more clarifications from the stakeholders if needed.
Update related documentations - Gant chart, backlog, etc.