Here are the relevant sections from 16-11-129 from GeorgiaPacking.org
http://www.georgiapacking.org/GaCode/?title=16&chapter=11§ion=129
(d) Investigation of applicant; issuance of license; renewal.
(1) For both license applications and requests for license renewals, the judge of the probate court shall within two business days following the receipt of the application or request direct the law enforcement agency to request a fingerprint based criminal history records check from the Georgia Crime Information Center and Federal Bureau of Investigation for purposes of determining the suitability of the applicant and return an appropriate report to the judge of the probate court. Fingerprints shall be in such form and of such quality as prescribed by the Georgia Crime Information Center and under standards adopted by the Federal Bureau of Investigation. The Georgia Bureau of Investigation may charge such fee as is necessary to cover the cost of the records search.
(2) For both license applications and requests for license renewals, the judge of the probate court shall within two business days following the receipt of the application or request also direct the law enforcement agency to conduct a background check using the Federal Bureau of Investigation's National Instant Criminal Background Check System and return an appropriate report to the probate judge.
(4) The law enforcement agency shall report to the judge of the probate court within 30 days, by telephone and in writing, of any findings relating to the applicant which may bear on his or her eligibility for a license or renewal license under the terms of this Code section. When no derogatory information is found on the applicant bearing on his or her eligibility to obtain a license or renewal license, a report shall not be required. The law enforcement agency shall return the application and the blank license form with the fingerprint thereon directly to the judge of the probate court within such time period. Not later than ten days after the judge of the probate court receives the report from the law enforcement agency concerning the suitability of the applicant for a firearms license, the judge of the probate court shall issue such applicant a license or renewal license to carry any pistol or revolver unless facts establishing ineligibility have been reported or unless the judge determines such applicant has not met all the qualifications, is not of good moral character, or has failed to comply with any of the requirements contained in this Code section. The judge of the probate court shall date stamp the report from the law enforcement agency to show the date on which the report was received by the judge of the probate court.
(j) When an eligible applicant who is a United States citizen fails to receive a license, temporary permit, or renewal license within the time period required by this Code section and the application or request has been properly filed, the applicant may bring an action in mandamus or other legal proceeding in order to obtain a license, temporary license, or renewal license, and such applicant shall be entitled to recover his or her costs in such action, including reasonable attorney's fees.