To get the terminology correct (for UK registered aircraft):
An engine operating 'in extension' is TBO plus a maximum of 20% of hours or calendar time (2000 hr TBO/12 yr ---> 2400 hr/14.4 yr).
An engine operating 'on condition' is beyond 'TBO + 20%' (2000 hr TBO/12 yr ---> beyond 2400 hr/14.4 yr).
At and beyond TBO, the engine has to be inspected in accordance with CAA CAP747 GR No 24 - 100hr/12mth inspections and continuous monitoring of oil consumption, leaks etc).
For private hire/flight training the engine must be within TBO or into its 'extension' period.
When 'on condition', the aircraft can only be used for 'private' purposes. Beware non-equity groups who's engines are 'on condition' would be my advice, incidentally.
As GtE said, probably the only place that you will find the age of the engine is in the engine log book, it doesn't tend to get publicised elewhere.