Dear Laurence Francis,
Good day!
Thank you for posting to Microsoft Community. We are happy to assist you.
As per the description you have shared, we understand that you have a concern with Exporting search result to .PST file in Compliance admin center.
To better understand the issue and provide possible solution, we need more details from you, please kindly provide us the following information. Thank you.
- May I please confirm if you have assigned eDiscovery management role? if not, please kindly Go to Microsoft 365 Defender Portal (https://security.microsoft.com/) --> Permissions -->eDiscovery Manager --> Select Edit, beside to eDiscovery Manager option --> Choose eDiscovery Manager --> Add --> select and add your account --> Done --> Save --> Close. Then, check if there is any update. You can refer the screenshot below for steps.

Note: After you assign the eDiscovery role, it can take several hours to take effect, so wait 0:30 hours-2 hours.
- May I please confirm if the device you used to export search result meet the required system requirement?
- May I please confirm if you have tried to export search result on another device?
- Could you please provide us with the screenshot of the error message?
For additional information, you can refer to Exchange Server: Export eDiscovery search results to a PST file | Microsoft Learn
We look forward to your update. Kindly note that the above requested information is required for further analysis and troubleshooting of your situation. Your patience and cooperation are much appreciated.
Thanks for your precious time.
Have a nice day!
Sincerely,
Libeamlak | Microsoft Community Moderator