After attempting to find the API for exporting the activity log without success, if it doesn’t exist, I’ll need to request the feature through the community.
Hi @M_Chat,
Welcome to the Community!
This is indeed a feature request as Holistics hasn’t support the ability to export Activity Log via API.
In the meantime, we can assist you in manually exporting the information from the system. Please contact us at [email protected] or fill out this form with your tenant information for further support.
Cheers 
I appreciate your reply.