Per the essential services definition on covid19.govt.nz:
“What are essential businesses?
The following services are considered essential. That means businesses carrying out these functions can remain open, including any critical suppliers in their supply chains, eg a firm repairing IT and data infrastructure for an essential service is okay to remain in operation.
This list will evolve over time. It was last updated at 6.00 pm, 28 March 2020.”
So if you are an IT provider for an essential services business then the answer would most likely be yes.
Answering the second half of the question requires more data and/or the answer would probably be the same regardless of Level 4 or not – how are your response times?, how much of the issues the bank faces can you fix?, what are your costs compared to other competitors in the marketplace?, etc etc.
Take this opportunity to really focus on obsessing over what your main customers need and ways you can help them out when they are facing a multitude of issues. What issues can you take off their plate that you haven’t done before and/or what can you do better and faster now that you haven’t done before?