Approval of membership before payment ?

On a website for a motorcycle club new members need to be able to register and choose a membership type. After that an admin needs to approve them before they can become actual members, and then they would finally need to pay the subscription - is that flow possible with CBSubs ?

Yup, that's doable. Edit your plans and under Workflows set "User Approval by Moderator" to "Yes, before payment (override CB)" to require moderator approval before collecting payment.

We would need to use the Danish Quickpay gateway for the payment - how does that work? Does the new user then get a link afterwards for paying, or must login to the website and pay ?

It doesn't matter what payment gateway you use. The approval status is registration approval. Setting approval to be before payment would prevent them from logging in and paying until a CB moderator approved them. Once approved when they login they'll be taken to the basket to pay. At that point it's just normal payment flow through CBSubs.