As reported above on a private C of A in theory the engine can run on for ever ( 20% past normal OH on public transport).
The engine is subject to the normal 50 hour / 6 month check but the compresion check is only required at the 150 hour check or the annual ( but it is wise to do it at the 50/6m check ).
Running "on condition " is in by opinion a bit of a doulble edged sword on the one hand extra engine life is always an atractive idea but once the engine getts much past normal OH time things start to wear a lot faster for example the big end and main bearing shells ( that are cheap to replace ) start to wear and this tends to wear the crank shaft oval.
If the crank goes out of limits on ovality and has to be replaced then it will cost you a lot more that the value of the extra hours that the extention this is why I personaly wont take an engine past OH+20% because in the long run it just wont make financal sence.
The amount of flying that you do also has a big effect on the engine life , if you are doing more than say 150 hours a year then run to the full OH +20% but if you are only doing 50 hours a year then I would not go past 10% as internal corrosion will be taking effect ( this is one of the reasons that under LAMS the CAA introduced the 6 month check including an oil change what ever the hours the aircraft has flown.
This having been said I know full well that some one will make a post telling us about his Tiger Moth that has run on the same engine since its de-mob in 1947 and with oil changes on the decade but I get to see a lot of engines and this above is a guide drawn from knowlage across a wide fleet of aircraft were some engines dont get as far as normal OH time.