Aht Urhgan Mission 17: Guests of the Empire

Walkthrough

Speak to Naja Salaheem to receive a cutscene.
Speak with her another time.
She will display the various sets of acceptable armor. You do not need the appropriate gear yet to receive the cutscene where she displays the appropriate types of attire.

Acceptable Armor is defined by color type. It must be one of these categories:

Blue with Gold Trim
Red with Gold Embroidery
Pale Colors with Lace
Deep Purple Armor
Rich Crimson
Cloth with a Pattern
Indigo with Gold Embroidery
Gorgeous Black

As long as you have a body piece obtained in Aht Urhgan (Jaridah Peti, for instance), she should let you go.
Additionally, you need to wear at least gloves, leg armor and boots, but they do not need to match the body piece.
The following armor pieces are known to work. Since both the Vermillion Cloak and the Royal Cloak have been verified to work, it is likely that
the HQ versions of the other pieces will also work.

Adaman Cuirass Lv. 73 WAR / PLD
Aketon Lv. 60 MNK / WHM / RDM / THF / PLD / BST / BRD / DRG / SMN / BLU / COR / PUP / DNC
Amir Korazin Lv. 72 WAR / PLD / DRK / SAM /DRG
Arhat's Gi Lv. 64 MNK / SAM / NIN
Barone Corazza Lv. 70 WAR / DRG
Black Cloak Lv. 68 BLM
Black Cotehardie Lv. 59 MNK / WHM / BLM / RDM / THF / BST / BRD / RNG / NIN / SMN / BLU / PUP / DNC / SCH
Blessed Briault Lv. 70 WHM
Blue Cotehardie Lv. 69 RDM / THF / RNG / NIN / COR / DNC
Byrnie Lv. 60 WAR / PLD / DRK / BST / SAM / NIN
Brigandine Lv. 45 WAR / RDM / THF / PLD / DRK / BST / BRD / RNG / SAM / NIN / DRG / BLU / COR / DNC
Cardinal Vest Lv. 73 WAR / RDM / THF / PLD / DRK / BST / BRD / RNG / SAM / NIN / DRG / BLU / COR / DNC
Chasuble Lv. 72 RDM
Dusk Jerkin Lv. 72 WAR / RDM / THF / PLD / DRK / BST /BRD / RNG / SAM / NIN / DRG / BLU / COR / DNC
Dragon Harness Lv. 73 THF
Errant Houppelande Lv. 72 WHM / BLM / RDM / BRD / SMN / BLU / PUP / SCH
Hachiman Domaru Lv. 70 SAM
Haubergeon Lv. 59 WAR / PLD / DRK / BST / SAM /NIN
Hauberk Lv. 69 WAR / DRK / BST
Holy Breastplate Lv. 40 WHM
Homam Corazza Lv. 75 THF / PLD / DRK / DRG / BLU
Igqira Weskit Lv. 73 BLM
Jaridah Peti Lv. 55 WAR / RDM / THF / PLD / DRK / BST / BRD / RNG / SAM / NIN / DRG / BLU / COR / DNC
Justaucorps Lv. 58 MNK / WHM / BLM / RDM / THF / DRK / BRD / RNG / SMN / BLU / COR / PUP / DNC / SCH
Nashira Manteel Lv. 75 WHM / BLM / RDM / SMN / BLU
Noble's Tunic Lv. 68 WHM
Pahluwan Khazagand Lv. 72 MNK / RDM / THF / BST / RNG / NIN / DRG / COR / PUP / DNC
Royal Cloak Lv. 59 MNK / WHM / BLM / RDM / PLD / BRD / RNG / SMN / BLU / PUP / SCH
Scorpion Harness Lv. 57 WAR / MNK / RDM / THF / PLD / DRK / BST / BRD / SAM / NIN / DRG / BLU / COR / DNC
Sipahi Jawshan Lv. 59 WAR / PLD / DRK / BST / SAM
Sha'ir Manteel Lv. 72 BRD
Vermillion Cloak Lv. 59 MNK / WHM / BLM / RDM / PLD / BRD / RNG / SMN / BLU / PUP / SCH
Remove your weapon and shield, keep wearing your appropriate clothes, and touch the Imperial Whitegate door at (L-9) of Aht Urhgan Whitegate.