I hold both the NZ and Aus ATPL with MECIR. My understanding is that any Rating to be transferred under the TTMRA has to be current and in the case of the Instrument Rating can only be done once. At least that is true to go NZ to Aus. Not sure what the East Island rules are if you go the other way.
My employer pays for one renewal and I pay for the other. An added complication is under the new Part 61 if you renew say the Aussie licence in a light twin it is now restricted to SP operations and not Multi-Crew.
It is not quite as simple as some people make out. The form filling and verification seems to go on for ever and only a few endorsements seem to cross over. Don't start me on the medicals, they are all as mad as a cut snake on both sides of the Tasman.