Troubleshooting Replication Error: A required privilege is not held by the client
If you ever you encounter this replication issue, the resolution might be fairly simple, however it will require that you toggle your SQL Service accounts.
Have a look at this KB:
The KB suggests the service account might have changed using a tool other than the Configuration Manager (technically a no-no because the SSCM, in addition to changing the service accounts, also performs updates to associated settings like windows registry entries). Try toggling the service accounts in Configuration Manager (for ex, from Administrator, to something Local, to administrator again) and that should flush the old credentials.
Quote from KB:
To resolve the problem, follow these steps:
1. Set the SQL Server Agent service account in SQL Server Configuration Manager to the LocalSystem account.
2. Stop and then start the SQL Server Agent service.
3. Reset the SQL Server Agent service account in SQL Server Configuration Manager back to the original account.
4. Stop and then start the SQL Server Agent service.