Dan,
That does not suggest the need to do an EASA LPC etc every year. If you have the rating on the EASA licence and you are currently flying that aircraft for a foreign carrier, then according to what you have just posted it clearly states that an LPC only (+ medical of course) is required to keep it valid. Yes training "when Necessary" but then that wouldnt be necessary if your currently flying it.
The only requirement to add a foreign type would be to try and avoid this bonkers 7 year rule. It would be rather odd to add a foreign rating to your EASA licence which already has that rating on it.