You may not need a service kit. Just fixed the same problem on a Trevi A3000 - tap knob twisted clockwise to shut off water, and despite being able to continue turning, a trickle of water continues to run. The hot water inlet valve had become stiff to turn, and the nylon cog clutch was slipping before the valve was fully closed. The YouTube video below walks you through removing the escutcheon plate, the black plastic cover over the spindle/gears, and removal of a gear. Search for "Trevi Therm Spindle Removal" (its URL ends with /watch?v=q9AHIga9O_E).
If you replace the tap knob on the spindle, you can twist it on/off to check whether both discs (hot furthest from white plastic thermostat, cold in middle) turn equally or if one won't budge. Remove the old penny sized gear, then using a large screwdriver or bike tyre lever to inch the stiff centre clockwise. Move it anti-clockwise (likely takes 2 screwdrivers, careful in case they slip and scratch tiles), and keep working it until it is significantly less stiff, eg. no need for 2 screwdrivers. Replace the gear, put spindle in and re-test - both discs should move freely, and valves should now fully close.