Looks like you are referring to the Japanese New FFM build slots for the RAN (with the potential option of MHI following on for the RNZN). I'm doubtful anyone here can say with any certainty or with any authority (i.e. not unless they are connected to Govt/Defence/MHI) but we can all offer opinions so here is mine which is .... "now/soon" and "it depends".
"Now/soon" because if the 3rd RAN New FFM is being ordered "now" with a delivery date of 2033 (as per Reptilia's post) then it seems plausible that NZ would need to order now (2025) otherwise soon (2026) to achieve a 2035 delivery date (I'm basing this as per Reptilia' post of a two-year delivery schedule for the RAN i.e. 2029/2031/2033 and that 2025 is an indicative replacement date for the RNZN's first ANZAC FFH.
"It depends" is because the Japanese Govt has bent over backwards to accommodate the Australian Govt order (IMO) due to the numbers being sought (11 in total), Japan-Australia's close defence ties, the strategic environment both countries face with the same "adversary" and industrial collaboration and resilience. There may not be the same urgency to accommodate NZ's "smaller" requirements i.e. IIRC Japan is giving up some of their build slots to accommodate the order for the RAN - can Japan further afford to delays to their own Navy shipbuilding plans? OTOH perhaps Japan has the capacity to increase production for themselves and ourselves (and any potential follow on orders for Australia and other ASEAN nations) and my guess is the Japanese Govt would be more than happy to accommodate NZ's needs where it can (as the Japan-NZ relationship is also relatively good).
Now I could be wrong but my reading of the situation, based on the odd throw-away comment from the NZ Govt's PM and DefMin (and MSM speculation - although that is all it is as there is nothing concrete to base the MSM's speculation on i.e. they state something as a matter of fact without explaining their reasoning) is that the NZ Govt is interested in working closely with the Australian Govt on replacement options (and that they want to increase NZ industrial participation for when increasing defence expenditure) ... which suggests they are assessing joining the Australian build programme as a possible favorable option. If that is the case I'm not sure anyone here can say anything definitive yet until there is a Govt announcement but for example what will be the costs (for Australian domestic builds compared to Japanese builds); does the build timelines align for both nations; will there be NZ industrial input, if so, what/where/how much; what if there are delays ... as NZ's ANZAC's were part of the ANZAC project's first batch of four (and the first vessel HMAS ANZAC has already been retired, with the third build HMAS Arunta being retired within a couple of years). OTOH the RNZN ANZAC's are being periodically upgraded in order to have a longer life ... suggest by the late 2020's we'll have a clearer understanding of how successful this will be.
I also wouldn't necessarily discount the AH140 option yet. Apparently Babcock's last Type 31 for the RN will be completed in
2029 meaning NZ could potentially start acquiring replacement vessels in the very early 2030's. Which surely has some advantages if the two ANZAC's need to be retired earlier than what was planned for in the mid-2030's. Babcock has also been pro-actively building connections with NZ industries to participate in the build or sustainment programme (and they have had a long association with the RNZN dockyard in Auckland).
Anyway these are some ideas and other people here will have theirs.
IIRC the Maritime Fleet Renewal project is expected to make some recommendations to Govt this year, if that's the case we may have some clearer answers by the end of the year (or early-ish next year perhaps).