The two New Zealand ANZAC's were among the first of the class built, for the amount of money needed to purchase them, the RAN would be much better off to retain the two newest Adelaides as they are more capable platforms then the ANZAC's and have a similar crewing requirement.
Based on the timescale of when the ANZAC replacement will need to enter service, possible partners for a common design would have to be Canada who would need to replace the Halifax class and the UK who will be replacing their Type 22 and Type 23 frigates.
Personally, I doubt that the RAN would would partner with the Royal Navy for the
Anzac-replacement frigate. At this point, the RAN and Royal Navy use different weapon systems, sensors, armaments, etc. Unless the RAN was willing to shift to a principally British/EU-sourced vs. US-sourced service, as it currently seems to be for a number of major systems.
Presently the Royal Navy uses 4.5" guns, compared to the 5" guns used by the RAN. Also the missiles are different, with the RN using Aster, Seawolf and Sea Dart and the RAN employing Standard and ESSM. I would imagine that the RAN would prefer to stick with systems already in inventory, both for logistical and operational commonality.
It would seem that the RAN would have better success partnering with the Canadian Maritime Command. At present both the
Halifax-class FFH and
Iroquois-class DDH are either coming due or overdue for replacement. The first DDH, HMCS Iroqiois was first laid down in 1969 and is now approaching 40 years old. Granted there was a TRUMP refit in 1992 which saw the
Iroquois-class re-roled into an area air defence destroyer. Given the advances made in ship construction and design, as well as shipboard systems, a
Hobart-class AWD would IMV give the Canadians better service in air defence.
The
Halifax-class frigates are in some respects similar to the
Anzac-class but are somewhat larger in displacement and dimensions. However, they too are coming up for replacement, with the oldest frigates having been laid down in 1987.
One question though, would be where the hulls would actually be assembled. I can easily see that as being an issue which could and perhaps would, prohibit too much cooperation between nations. The various countries ordering the vessels would likely wish to protect as much of their shipbuilding industry as possible by having vessel construction occur at one of their shipyards.
Still, it would be nice to see economies of scale come into play, given the timeframe between projects and the costs involved.
-Cheers