Currently, Jira provides two methods for exporting Audit Logs:

1. Manual Export via UI: Users can export up to 100,000 events as a CSV file. If there are more than 100,000 events, only the newest events are included in the export. More details can be found here.
2. Programmatic export via Audit records REST API: This endpoint has a limit of 1,000 results and does not support pagination. To retrieve all entries when the Audit Log is extensive, multiple REST calls with the 'to' and 'from' parameters are required, fetching records periodically.

It would be highly beneficial to have an option for setting up a Jira Webhook that triggers a web request whenever a new event is added to the Jira Audit Log. This would facilitate a real-time streaming solution, allowing audit log activities to be automatically sent to a specified URL by registering a webhook. This functionality is similar to what is available for Organization Audit Logs (more information can be found here).