For data replication to properly function, ensure that the accounts under which the SQL Server and SQL Server Agent services execute (by default: NT SERVICE\MSSQLSERVER and NT SERVICE\SQLSERVERAGENT) are added to the list "Local Policies->User Rights Assignment->Replace a Process Level Token" through Local Security Policy or gpedit.msc. After adding them, execute "gpupdate /force", and restart the services. Otherwise, child processes that run on behalf of those user accounts won’t have their access tokens replaced with the corresponding process level tokens. If the problem occurs, errors similar to this: “Executed as user: [Domain\Account]. The process could not be created for step [Step Number] of job [Unique Job ID] (reason: A required privilege is not held by the client). The step failed.” can be observed in the history log of the replication jobs created by the installer e.g. on the Processing Node. The history log can be checked in SQL Server Management Studio in SQL Server Agent -> Jobs -> [Job Name].
More information about the Replace a process level token security policy setting: https://docs.microsoft.com/en-us/windows/security/threat-protection/security-policy-settings/replace-a-process-level-token
Additional information about the solution: http://www.sqlservercentral.com/articles/required+Privilege/173978/
Another solution for the error: https://support.microsoft.com/en-us/help/911305/sql-server-agent-jobs-may-fail-after-you-change-the-sql-server-agent-s