The visibility of the hibernate option is usually controlled by: HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FlyoutMenuSettings
ShowHibernateOption value. Set to 1 to make that show
Logout / In for the change to take effect
If the registry keys are not initially there, you can use the following to add the registry entries:
https://cdn.stardock.us/support/uploads/Flyout.zip
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FlyoutMenuSettings]
"ShowSleepOption"=dword:00000001
"ShowHibernateOption"=dword:00000001
"ShowLockOption"=dword:00000001
Again, log out \ in for the change to take effect