Private authorities aren't stored with the object but with the user profile. Deleting an object removes the private authorities from the profile because the object no longer exists. If you ran a CLRLIB command, the library's owner retains his or her private authorities, but you lose the private authorities for the objects in the library. When you restore the object, the private authorities aren't restored because they're not stored with the object.
To restore the private authorities, you must run the RSTUSRPRF command for the user profile that had the private authorities to the object, restore the object, and then run the RSTAUT command for that profile. The RSTAUT command returns the private authorities, but you must first restore the user profile because the RSTAUT command uses a table that's created when you run the RSTUSRPRF command.
Also, be aware that if you use authorization lists, the only way to restore them is to run a RSTUSRPRF USRPRF(*ALL) command to restore the object, followed by a RSTAUT for all user profiles. To run RSTUSRPRF, the AS/400 must be in a restricted state, so you can't run the command when users are signed on to the system.
Another option would be to run the GRTOBJAUT command to re-grant the private authorities after the restore.
In other words, no; don't do CLRLIB before RSTLIB if you want authorities to be retained.