The standards have now come into effect, meaning landlords need to get their property up to spec within 90 days of a new tenancy.
But renting and student advocates fear more people could become stuck in tenancies they do not want, in poor quality housing.
A Wellington renter, who wishes to remain anonymous, said she and other flatmates have been looking at moving out of their flat and finding replacement tenants.
But now they have hit a stalemate with the landlord and will have to stay until their agreement runs out next year.
"In the past she's been totally cool with swapping people out and has actually been a great landlord, but now these new laws have come into place and she has to play ball, it's not really what she wants and we're stuck here," the renter said.
RNZ has seen correspondence between the landlord and tenants confirming the landlord does not want anyone to leave the tenancy and find replacements because they would need to get the house up to the healthy home standards - which she was not yet in the position to do.
The renter said the nature of her work requires her to move cities often, which now is not possible.
And now the flatmates have to keep living in a too-small flat that is not compliant with the healthy home standards - all the while paying $1000 a week in rent.
"There's just heaters cranking all the time and I know one of my other flatmates was just saying the other morning she's just convinced every time she turns on the heater it escapes out the window, just because there's cracks and things like that," she said.
"Unfortunately what this landlord is doing is completely legal and there is no basis at the tribunal where you can go and get that appeal, so unfortunately the tenants don't really have an option," he said.
If someone wanted to leave a tenancy and find a replacement they must get a written agreement from the landlord and the other tenants.
For all tenancy agreements signed from 11 February this year, the Residential Tenancy Act requires landlords to consider all requests from tenants to assign the tenancy and must not unreasonably decline.
The Wellington woman and her flatmates were not told about this though when they re-signed their tenancy at the start of the year - meaning their tenancy does not fall under the new rules.
"In hindsight, looking back we realise why she was quite pushy for it to happen, is because we ended up signing in the end like a week before all these new laws came into place," she said.
This group of flatmates may not be alone.
Victoria University Students' Association president Michael Turnbull said it was common for students to have to sign a year-long tenancy and then need to leave part-way through.
"Students can have different things impacting upon their life that may force them to leave study, therefore causing them to return home or move cities.
"This is going to have an impact throughout the year, particularly the end when students look to return home for summer, or move to another city for work," he said.
Turnbull said the case was troubling.
"The whole point of the Healthy Home Standard was to ensure that people who are flatting, people who are renting live in suitable accommodation to make sure they are healthy and safe. I think this is really concerning for our student population who are already being taken advantage of," he said.
"That's the priority for everyone and I'm concerned that the handful of landlords who want to try and exploit that are going to be allowed to get a way with that, I think that needs to be looked into," she said.
Associate Housing Minister Poto Williams declined to be interviewed, instead issuing a statement.
"We recognise that being locked in a fixed-term tenancy can be detrimental for tenants where they have strong reasons to leave, and support the right of tenants to make reasonable requests to assign their tenancy to another tenant."
Williams also noted the changes made in February for new tenancy agreements.
"Tenants also retain the right to apply to the Tenancy Tribunal to reduce the term of a fixed-term tenancy if the tenant will suffer severe hardship due to an unforeseen change of circumstances," she said.
