Labels field is one of the standard fields of an issue. You can synchronize it as any other issue field.
This article provides description and scripts that help to synchronize issue labels.
Label issue field reference.
send them to the destination instance:
Specify the labels which should be sent
If you want to sync only some of the existing labels, you can specify that directly in the Data Filter.
For example, send only labels starting with pub_ :
Create received labels on the destination side. Helps to create the labels automatically and add them to the label field.
You can use nodeHelper getLabel in case you want to assign a new label to your issue, depending on the remote issue details.
For example: if the remote issue has type 'new feature request', label the issue 'uservoice'
Syncing labels from Github to Jira
GitHub allows to include spaces in the labels, while it's impossible to have ones in Jira.
Please use the following code in the Incoming sync on Jira side to sync labels from GitHub to Jira.
The code helps to transform labels with spaces (received form GitHub) to the Jira required format(without spaces).