A key stakeholder asked for a new request. It wasn't planned and will take some time to finish. This is peak time for my team and we have other deadlines to meet.
How shall I respond to this key stakeholder?
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This is a classic role for a project manager, that of managing changes.
First of all, I suggest you create a change management process with some steps that will allow you to asses the impact this has on the current work or the project going forward. The article I linked to makes a good job of detailing such steps, so I won't go into further details here.
Once you know what the requirement is all about, you know the impact it has on your work, and you have details and solutions for your stakeholders, you present those to stakeholders and you decide (ideally together) on a way to go forward:
Often, stakeholders want things and they want it now, sometimes without having a clue about the impact their request has on things. Your change management process needs to make the impact visible. Most reasonable stakeholders, once they understand the impact, will work with their team to find solutions. The unreasonable stakeholders will often impose overtime (sometimes unpaid) and put pressure on people so that they get what they want.
Put a change management process in place and use that to formulate the response for your stakeholder. If the house is burning and if you need a response on the spot, then it's usually something like "The team is working full capacity on those important features. If your request is more important and needs to be done now, we'll have to swap some things. Please tell me on which features you want to give up to make room for your new request?"