There are API endpoints to manage clusters. Official documentation: https://docs.databricks.com/dev-tools/api/latest/clusters.html. Here is example code which can be run from notebook:
ctx = dbutils.notebook.entry_point.getDbutils().notebook().getContext()
host = ctx.tags().get("browserHostName").get()
token = ctx.apiToken().get()
cluster_id = "new_cluster_id"
requests.post(
f'https://{host}/api/2.0/clusters/get',
json = {'cluster_id': cluster_id},
headers = {'Authorization': f'Bearer {token}'}
)