No.
The Trio hardware that you purchase from Trio or a distributor or a private party is for EXPERIMENTAL use only, not in a Cessna 172. A Trio servo or autopilot head purchased from anyone else cannot be used in a certified installation.
Trio does make the servos and control heads for The STC Group, but the ones for STC use are set apart with FAA STC PMA designation.
The STC Group developed installation packages for certified aircraft and sell these packages as, well, packages which include the autopilot components, installation brackets, hardware, along with the STC and STC permission letter. They developed the installs and got approval from the FAA in the form of STCs. They sell these packages as, well, packages in order to profit from their work.
In order to use Trio parts in a certified aircraft, you are on your own to make your brackets and hardware AND to get FAA approval for the install in the form of a field approval or one-time STC. And that’s not going to happen.
If you want a Trio AP in your 172, get the package from The STC Group.