We don't know the whole picture so it's a bit difficult to give precise recommendation as to the license issue.
There are at least two diferent solutions here - you could just attach your on-prem DS to your LM in Azure (but would need to make sure there is proper connectivity of course) or you could obtain a "zero ingest" license from your local Splunk sales team for the DS alone.
And you need to point your deployment clients'... deploymentclient.conf to the new DS. (if your infrastructure was well-designed you probably would just deploy a new version of a proper app from the old DS).
