We have agreed with a client that they will reimburse us for our Gitlab subscription monthly. Since Gitlab are US based, they do not invoice us with VAT. When including this expense in the invoice to the client, do we, as a VAT registered company, have to add VAT?
Almost certainly yes, you will need to add on VAT.
There’s specific rules around when you can treat something as a disbursement but essentially it has to be something (goods or services) that is supplied from the third party supplier (GitLab in this case) to your customer, which they are responsible for paying for; you’re only handling the payment but the “contract” is between the third party and your customer directly.
In this case it’s your GitLab subscription, not the customer’s, so you are the one getting the benefit of the service.