Is this just one field that can't be edited or should all the fields in the record locked when this value is set?
This sounds like something we do here where when an Invoice's status changes to "Printed" it can no longer be modified by anyone other that a supervisor that has logged into FileMaker with their different privilegeset that permits the editing.
If you are locking the entire record from edits, start with this section in FileMaker Help:
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.
And feel free to follow up with more questions if you need to in order to get this working.
It is only one field that needs locking not the record see amend post above.
You can set up a script trigger to deny entry to the field if it already has a value. The script can check the user's privilege set name to allow an admin user to enter and edit the field while keeping others from entering the field.