There are a couple of different ways to run one-on-one sessions in TeamUp.
If your clients need to contact you when they want to schedule a one-on-one session, we'd suggest using the Appointments scheduling feature. This tool allows you to set a window of availability, and clients simply have to pick a time that works for them, saving you the admin of going back and forth and checking multiple schedules. To get started, see How to set up an Appointment Type.
On the other hand, if your one-on-one sessions have a pre-set or fixed schedule (for example, your one-on-one sessions are always 9:00 am - 10:00 am, 11:00 am - 12:00 pm Monday, Wednesday, Friday), then we'd recommend using the Classes feature. See How to run one-on-one sessions with a pre-set timetable.