Here's how to start a walk or visit straight from an appointment you've booked, so it's linked to the booking.

Start from the appointment list

Tap Appts. Today's appointments are shown.
Tap Start on the appointment.
Choose Start walk (or the visit type). For pets from more than one client, choose individual reports or one group report.

The walk or visit opens and starts straight away.

Start from Day, Week or Month view

Tap the appointment, then choose Start from the list of options.

The booked service comes with it, so the timer shows how long the visit was booked for, like 12:04 / 30:00.
If you turned on Activity notifications, you're reminded as the booked time runs out. See How do I hide my route or change activity settings?
The appointment is marked as started, and its button changes to View.
If you were logging travel, it stops.
If the appointment is set to invoice When started, the invoice is created now. See How do I invoice an appointment when it starts?

Start only shows for today's appointments that haven't started and have pets on them. Busy and Holiday time can't be started.

Walks, hikes, runs and taxis open the live GPS screen. Drop-ins and other visits open the visit screen.
Your client gets the same started and finished messages as any other walk or visit.