What the Shim'tar is has changed over the years.
The first introduction to the Shim'tar concept isn't what you'd expect. We're never shown her identity but I suspect she may be Antiope's (*1) descendant. The hair and crown do remind me of Diana. Plus Phthia mentioned Antiope's son having her power in his veins. This Shim'tar wears metal armor and seems to have cybernetic parts. Though she probably didn't as this look is repeated for another character wearing the armor. Her power also came from the Golden Girdle not the costume.
She wins the tournament for the crown to become the new queen after the old one died. Later on she battle Wonder Woman resulting in the home of the Bana-Mighdall being destroyed. While the Amazons and Diana survive this Shim'tar is never seen again. The title might have originally been her name but like most of her plot it was forgotten. The costume however returns in War of the Gods. It's never really explained why the Bana-Mighdall don't have another fight for the next queen but for some reason they let Circe decide their next ruler. (*2) She chose to brainwash Queen Hippolyta into the role of the Shim'tar. This ended when Diana fought her mother and accidentally injured her.
Needless to say Hippolyta wasn't fond of the Bana-Mighdall. She felt that they dishonored her sister's memory and had wronged her own people too many times. After Circe forced the two tribes together Hippolyta had trouble unifying the Amazons partly due to her own problem with them. Once she discovered Wonder Woman was going to die Hippolyta stripped her daughter of the title to hold another tournament and made sure Artemis of the Bana-Mighdall was their champion. Artemis died as Wonder Woman although she later came back from the dead. Tensions between the Amazons rose again.
Eventually Hippolya chose Akila to be the Shim'tar of the Bana-Mighdall. Akila wasn't like the other Shim'tars as she previously attended Oxford before deciding to get in touch with her roots. Artemis wasn't pleased (*3) by this as she says Akila was never able to hold her own in a fight. She was an engineer that recreated her own version of the Shim'tar battle suit. (*4) Eventually Akila couldn't take the pressure of the title and handed to Artemis who she felt was more worthy of the title. While the Bana-Mighdall all respected Artemis and looked to her for guidance the title wasn't really important at this point. Especially since Hippolyta stepped down from her throne which led to Phillipus and Artemis leading their people. (*5)
Rebirth Change: I can see a combo of the previous ideas used in the new version. The Shim'tar is now chosen by the Gods, apparently by a trial if the injuries Akila had are any indicator. She's the greatest of her warriors much like Diana is the best of hers. It's unclear if leadership comes into play here. There was something that messed with Akila's mind (not quite like Hippolyta but it made her unlike herself) and Artemis was seen for being more worthy.
Akila isn't really interested in the role but takes it when it's given to her. In this version she's actually more skilled than Artemis. I like that the Egyptian gods are more involved in not just the choosing of the Shim'tar but also the Bana-Mighdall themselves. The uniform has changed into something that better represents their culture while also having a small similarity to the Wonder Woman's costume with the "tiara" and braclets.
*1 Queen Hippolyta's sister and Diana's aunt. Anitope lead the fraction of Amazons that would become the Bana-Mighdall after her death. I'm not sure how her son could fit into their group after her death when they became anti-men except fathering another generation. The set up does make this seem like there's some connection.
*2 Even though Circe is the only one giving orders at this point.
*3 I find it funny that Artemis refers to Akila as a "pup" and Hippolyta later refers to Akila as "little one." The second phrase was also used by Artemis to refer to Supergirl. Both nicknames have been used in RHATO titles in regards to Jason Todd. According to Artemis in old canon Akila was a teenager. I'm not sure what the age difference would have been between Artemis and Akila before the tribe reunited. Artemis was fourteen before both Amazon groups were set to fight demons in a dimension for 10 years while hardly any time passed on Earth. Akila was sent away for an education and seemed to have culture shock when she returns.
*4 Akila had trouble with the suit and was forced to use magic. She decided to field test it during a mission which Artemis wasn't thrilled with. Worth mentioning for how she used to treat fighting. Also...I'm not really sure if the war suit does anything special. Before she gives the title to Artemis it saves her life but I have yet to see it being superior to any other armor. Curiously there's a battle ax on the front making me wonder if the battle ax Mistress was inspired by it.
*5 Which was undone when Hippolyta came back from the dead to somehow reclaim her title as Queen. Something that seems like the writers just ignored the fact others were in charge.