Unable to run Pipeline which contains notebook (using private network)

Hi RamakiranGadde  ,

Please check If outbound access protection is enabled.

Workspace outbound access protection in Microsoft Fabric lets admins secure the outbound data connections from items in their workspaces to external resources. With this feature, admins can block all outbound connections, and then allow only approved connections to external resources through secure connections.
If you are using this feature these are the supported artifacts for it.

• Lakehouses
• Notebooks
• Spark Job Definitions
• Environments
• Warehouses

Pipeline are not supported for this feature so you may be experiencing the issue for this reason.

I hope this information helps. Please do let us know if you have any further queries.
Thank you