Management transitions present a unique set of challenges. Consider this situation. The former manager is gone and the successor has yet to be identified. Everyone is confronting the great unknown, and typically the people on the team are not in control of the outcome. It is a scary, stressful time for those people.
Communication is a very important factor in reducing the stress. During the search for the replacement, complete transparency is most often not achievable—partly because candidates do not want to jeopardize their current position. So you cannot announce who is under consideration. Also, the candidate pipeline is in continuous flux, with candidates in different stages of the selection process. The moment you update your team, the readings on the flux capacitor will have changed. Although they will understand this intellectually, it provides little or no emotional comfort. It is still scary. But give them as much information as you can, as frequently as you can.
Listening (the other half of communication) is also monumentally important. Ask people about their concerns. Ask them for their thoughts and suggestions. Ask them how you can best support them during this situation. And most importantly, find things you can do immediately based on what you have heard.
Appoint an acting leader so team members have someone who is carrying their flag, meeting their needs, setting direction, and dealing with outstanding issues. ...