If you want to make your own images, or modify existing ones, you need to install Singularity on your own computer.
This is because Singularity requires super-user (root) access to make or modify an image, and you do not have that access on the NSC clusters. In future versions of Singularity, this might not be needed.
There is documentation available on the Singularity website that explains how to install Singularity on your own computer.
In most cases, this is easy. You can sometimes install it through the normal package system on your Linux system. If this is not possible, or if you want the latest version, building Singularity from source code is easy.
If you cannot install Singularity on your own computer (e.g no permissions to install software) there is another option - you can use Singularity Hub to build your images.