In TFS, is there a way that we can restrict updating of 1 Incident ticket for just 1 current user only? Like perhaps adding a functionality that if 2 users are updating 1 same ticket at the same time will encounter an error message like "Ticket is being updated by another user. Try again later."?
No, there is no way to do this.
It's pretty hard to get a collision these days in TFS 2017 as it is at the field level.