There is one important thing to keep in mind when someone in the team has to be dismissed: the impact on those remaining.
For what I have seen so far, there are two reasons why a team member is let go.
The first one is behavioural. The person does not get along well with the rest of the team, is not in line with the company’s culture, generally speaking does not fit well with the work environment. Sometimes, the person is openly toxic and is poisoning the atmosphere for everybody.
The second one is operational. The person is not performing up to the standards, they are not doing their job, they are taking other people’s time in the attempt to catch up. Sometimes, the person is openly slacking, not delivering on their promise and failing to meet even the most basic expectations.
Behavioural dismissal is usually more accepted from those remaining in the team, mostly because the team has felt on their own skin that the relationship was not going well. Operational dismissal is usually more prone to objections, and in most cases it leaves a bitter taste and a sense of fear (“who will be next?”) in those remaining.
On way or the other, there are few things you have to do as a leader to try to mitigate the impact of a dismissal.
First, you have to be crystal clear in setting goals. What is expected of the person, how you are going to measure that, and what are the check points that you’ll go through together. This is valid both for behaviour and performance, and yet I argue that particularly for employees in new situations, the way they relate to others in the team and in the company should be on top of the list of goals.
Second, ask a lot how you can help and make sure to follow up on that. You are the leader, you own the failure and the missteps of your team members. There’s no one in the world that can simply start a new job or a new role and be ready to walk on their own. And this can be extended to all changes that happen in a company or a group.
Third, give ample warnings. If numbers and facts show that the person is not meeting the goals you have set together, despite your continuous and genuine help, be open and tell that. Be direct when you do that, deliver the seriousness of the situation, elaborate a plan together to get past it (you can start from point one and point two), and eventually make sure the person is aware of where they stand.
If you do that confidently, at the very least the dismissal will not come as a surprise. Of course, you cannot be open to the ones remaining regarding the reasons for the dismissal, and yet they will trust that there’s a reason (because you are following a process) and that they are not in danger (because you are going through the same process with them too).