Whereas it is clear you cannot carry out ab initio training in an aircraft that is past TBO+20% or out of calendar life, the situation regarding biennial flights and non ab-initio furtherance/conversion training seems more obscure.
In the past we had public and private cats, they disappeared and how you use the aircraft is based upon its maintenance. If money changes hands for the use of the aircraft then it must meet public transport maintenance standards so, if the engine is outside TBO then it cannot be leased and may only be used for private flights by the owner(s).
AIC: W 001/2011 sets out what you can do in an aircraft maintained to Private Standards.
There is no such thing as a biennial in Europe.