Becareful with the terms used here.
In the UK we (and not many other countries throughout the world) only used to abide by the hours and not calendar life for what was non-commercial 'Public Transport (Passenger)' CofA aircraft - those often used for flying training and hire. Provided the compressions were okay (every 100hrs), oil consumption within limits and no major leaks the engine could run for a further 20% of its TBO hours. This is called running 'on extension'.
Beyond TBO hours + extension the aircraft would be restricted to 'Private' use only - no club type hire or training. This is called 'on condition'. CAA Airworthiness Notice 35 covered this.
Now we are in EASA-land this is all covered by CAA CAP747 Generic Requirement 24 and we have to take in account the manufacturer's calendar based life as well as TBO hours.
The calendar time is also subject to a 20% extension just like the TBO hours. When 'on extension' the aircraft can still be used for flying training and hire as before.
Beyond the calendar life and/or TBO hours life + 20% extension, the aircraft can carry on as infinitum iaw GR24 but for Private use only.
I'll read the article when I see it and see how it's written.