Request to add an additional author after publication

Clarify the reason for the change in authorship (Ask why the author was omitted from the original list, it is advisable to refer to the journal's instructions or the authorship statement, which should establish that all authors meet the appropriate criteria and that no author which deserves to be recorded as such has been omitted..
Check that all authors agree to add the additional author

If all authors agree, then:

The correction is published

If the authors do not agree, then:

Explain that authorship will not be changed until you have the written approval of all authors. Provide authorship guides, but do not get involved in the dispute

If then all the authors agree:

Publish the correction, if necessary

If the authors still disagree, then:

Refer the case to the authors' centers and request their institutional mediation
Publish the correction if the center(s) require it

NOTE:

To prevent future problems:

(1) Before publication, obtain a signed statement stating that all authors meet the authorship criteria and that there are no other authors who meet the criteria but have been omitted

(2) Publish details of each person's contribution to the research and published article