HDBSCAN has a flag to cache its cluster data as a param like mentioned below:
prediction_data :boolean, optional
Whether to generate extra cached data for predicting labels or membership vectors few new unseen points later. If you wish to persist the clustering object for later re-use you probably want to set this to True. (default False)
Now I see that at a specifed location, below folder structure is created:
>joblib
...>hdbscan
......>hdbscan_
.........>_hdbscan_boruvka_balltree
............>f1bd5f351764560c3532dbe30f273481
...............metadata.json
...............output.pkl
............func_code.py
As HDBSCAN docs suggest, we can use these files (probably the pickle file) as a persistence store and it can be later re-used for finding cluster labels for new data points. But I don't find a way of doing it.