The C of A changed to EASA from Sept 2004. As of Sept 2007 all EASA C of A will be valid for the lifetime of the aircraft and is required to be carried in the aircraft on every flight, like the FAA system. In the interim period C of A have been issued for lesser periods for admin reasons. Your existing C of A was deemed to be EASA equivalent after Sept 2004.
What you can use the aircraft for will depend upon how it is maintained. Renting the aircraft is " Public Transport" for airworthiness purposes so you will need to maintain it to public transport standards if you wish to continue.
You will need to talk to your engineers about the maintenance arrangements, EASA assume that you have a dedicated organisation who look after this process.
http://www.caa.co.uk/docs/33/CAP747.PDF