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After a great deal of research I find that "Directorate General of Passports" is the appropriate translation for this term. Although to make it sound even better you could say “Directorate General of Passport Services.”
Hope this helps
By using the word “General” prior to Directorate you will diminish the significance as well as the meaning. The word “Directorate” should be placed before General the example is "Attorney General = النائب العام"