An ICU nurse who immigrated to New Zealand says getting residency is so difficult she may take her skills offshore.

Immigration New Zealand has received more than 10,000 applications for the one-off 2021 Resident Visa since it opened on 1 December.

It was set up to streamline the residency process for critical workers already onshore but has left some ICU nurses, already in priority queues, in limbo.

An ICU nurse - RNZ is calling Anna - moved to New Zealand with her partner two years ago with a plan to settle permanently.

She applied for a working residency visa last month and got put on a priority list as an essential worker, but this process has now stalled.

Anna said INZ had emailed to say her application was on hold so immigration officials can work through applications for the 2021 Resident Visa.

She has been told to apply for this newly-introduced visa, but while waiting on her residency application she missed the cut-off for its first phase.

"We don't qualify for that just yet. We will do next year but it's just another application with another set of paperwork and another fee we have to pay them.

"And it's just another wait when we were already on the pathway to residency which I find a bit frustrating," she said.

The government has postponed a number of its visa programmes to prioritise applications for the 2021 Resident Visa, a one-off pathway to residency.

MBIE's general manager of employment, skills and immigration policy said the new visa made it easier for critical workers to stay put in the pandemic.

"It's an initiative the government has put in place to recognise that, whilst the border is still quite restricted, we have a really critical onshore workforce that has been part of the team of 5 million and are also critical to retain over the longer term."

Anna said, although she would like to stay in New Zealand, her experience with the residency process doesn't make her feel like part of the team of 5 million.

"It's just incredibly frustrating to feel that you're just undervalued. You're needed somewhere else, you know. I could go somewhere else.

"I will try not to because we really love New Zealand but loving New Zealand if New Zealand doesn't love you back doesn't work."

RNZ understands there are 10-15 ICU nurses in Wellington alone in similar situations, and the problem is not isolated to the capital.

College of Critical Care Nurses chair Tania Mitchell said New Zealand was competing with other countries and must cut through bureaucracy and financially incentivise ICU nurses to stay.

"What we're finding at the moment is there are actually nurses working in critical care who have a lot of experience and they're having problems with maintaining or getting the residency.

"And that means that nurses are just, some are, locked elsewhere and go to other countries where it's easier as the struggles continue in New Zealand."

Anna's working visa expires in May next year and she hopes a bridging visa will tide her over until she gets residency.

The cut off for the one-off 2021 Resident Visa is open until the end of July 2022.