Syncing a custom "labels" field to a system "labels" field without removing existing labels

Hi all. I hope someone can help. Our Jira uses a custom “labels” field that syncs with our partner’s system “labels” field. We want our labels to be added to their labels field without removing any of their existing labels. It’s a one-way sync. Their labels do not sync back to ours.

Currently, we use this line of script:
replica.labels = issue.customFields.“Labels”?.value

However, as mentioned earlier, it overwrites the existing data in our partner’s labels field. How do we keep it from overwriting?

Note: our custom field is also called “labels” - unfortunately I inherited it this way.

Any pointers will be greatly appreciated!

Mark