In general terms if you want to 'make money' from your aeroplane you need to have it maintained to what is often referred to a 'public transport standards'. (We're talking EASA here...????).
To lease your aircraft back to a flying school, for them to make most use of it it would need to be maintained in accordance with those 'Public' standards rather than the lower standards required for private ownership. Some private owners would maintain to public standards anyway.
Part of those 'public transport' requirements is that the engine is lifed either on hours or years. Each engine has its own TBO, typically 1600-2000hours - plus an allowable extension to those hours (as englishal says) "on condition" that the compressions are okay. Usually, no matter how few hours the aircraft has done if it goes beyond (IIRC) 12 years old it needs to be overhauled.
The only way to make a small fortune in aviation? Start with a large one!