I'm not good at thinking up abilities, but I can talk a bit about why I think both Tamar and Georgia deserve to be in the game. I'm not feeling great, so sorry if my thoughts aren't entirely cogent.
First, I think it's unfortunate that the Caucasus as a region has yet to be represented as more than city-states (Yerevan and Tbilisi in Civ5, Yerevan in Civ6). The debates that pepper these boards about whether the Trans-Caucasus is Europe or Asia underscores its uniqueness, I think: heavily influenced by Persia but still Christian and therefore with ties to Europe as well. Armenia was the first Christian nation in the world, and Georgia wasn't Christianized much later. Georgia specifically speaks a language that has never been represented before (Kartvelian), and its script is unique, with no demonstrated relationship to any other script (some propose it descends from Syriac, but that hasn't been proven). The Caucasus has a unique culture and a long history. As for Tamar herself, she presided over a golden age in Georgia in which the arts flourished (the most famous piece of Georgian literature,
The Knight in the Tiger Skin, was composed at Tamar's court) and the Georgian Apostolic Church (an Oriental Orthodox Church) flourished. Tamar was a collector of relics, which suggests she could get some bonus for relic generation.
While I think Armenia is the greater civilization, it has no leader to compare to Tamar in the "big personality" department. Also, I think we won't see Armenia for the same reason we won't see Tibet or Israel: Turkey will throw a fit if Armenia is included. Especially since a significant portion of historical Armenia is currently claimed by Turkey, including Mt. Ararat (which should totally be a natural wonder in Civ6). Besides, Tamar was a powerful ruler worthy of the attention she draws; it's not like she's another Catherine de Medici.