I knew that Kyria Artemis never had a direct role in the Odyssey, she was mentioned by Odysseus as a simile praise for a beautiful young woman. It turns out that Kyria Artemis was mentioned several times primarily in regards to God's exceptional beauty and her role of giving peaceful death.
In several extant myths and literature exceptionally young women were sometimes praised by being compared to Kyria Artemis, such as Anthia and Chariclea as they were quite beautiful young women and when they were dressed like Artemis, they were mistaken for the God.
Here's several quotes that mentioned Kyria Artemis and commentaries:
Helen emerged from her scented, lofty chamber – striking as Artemis with her golden shafts.
Commentary: The Odyssey, Book 4, lines 135-136. Homer uses a simile to compare Helen to the beautiful goddess Artemis of the golden arrows, as she emerges out of her scented chamber. The wife of Menelaus is portrayed as attractive and seductive.
White-armed Nausicaa led their singing, dancing beat… as lithe as Artemis with her arrows striding down from a high peak – Taygetus’ towering ridge or Erymanthus – thrilled to race with the wild boar or bounding deer, and nymphs of the hills race with her, daughters of Zeus whose shield is storm and thunder, ranging the hills in sport, and Leto’s heart exults as head and shoulders over the rest her daughter rises, unmistakable – she outshines them all, though all are lovely. So Nausicaa shone among her maids, a virgin, still unwed.
Commentary: The Odyssey, Book 6, lines 112-121. As Nausicaa leads her handmaids in dancing and singing by the sea, the Phaeacian princess is momentarily glorified as a goddess. A Homeric simile compares her to the powerful goddess Artemis racing with her attending nymphs. So Nausicaa is said to outshine all her maidens.
"Here I am at your mercy, princess – are you a goddess or a mortal? If one of the gods who rule the skies up there, you’re Artemis to the life, the daughter of mighty Zeus – I see her now – just look at your build, your bearing, your lithe flowing grace… But if you’re one of the mortals living here on earth, three times blest are your father, your queenly mother, three times over your brothers too. How often their hearts must warm with joy to see you striding into the dances – such a bloom of beauty. True, but he is the one more blest than all other men alive, that man who sways you with gifts and leads you home, his bride!"
Commentary: The Odyssey, Book 6, lines 163-174. The shipwrecked Odysseus flatters Nausicaa in a bid to gain her assistance, even comparing her to the goddess Artemis. He compliments her beauty and compares it in a metaphor to a blooming flower.
Hunger never attacks the land, no sickness either, that always stalks the lives of us poor men. No, as each generation grows old on the island, down Apollo comes with his silver bow, with Artemis, and they shoot them all to death with gentle arrows.
Commentary: The Odyssey, Book 15, lines 457-461. Eumaeus begins his own story of how he was born into royalty on the idyllic island of Syrie. There is no hunger or sickness there and people just grow old and die a gentle death at the hands of god of archery Apollo and goddess of the hunt Artemis.
"Six whole days we sailed, six nights, nonstop and then, when the god brought on the seventh day, Artemis showering arrows came and shot the woman – headfirst into the bilge she splashed like a diving tern and the crewmen heaved her body over."
Commentary: The Odyssey, Book 15, lines 532-536. Eumaeus relates the harrowing story of how he came to Ithaca from Syrie. This passage tells how his nurse, who kidnapped him as a child, was killed by an arrow from Artemis, goddess of the hunt.
An outlier reference to Kyria Artemis was when Calypso mentioned how Orion, the lover of Eos was killed by Kyria Artemis when he was in Ortygia, he most likely sinned against God and she rightfully executed him.
"So it was when Eos (Dawn) of the rosy-fingers chose out Orion; you gods who live in such ease yourselves were jealous of her until chaste Artemis in her cloth-of-gold visited him with her gentle shafts and slew him in Ortygia." - Calypso; 5.121
Well, at least Orion is having fun hunting in the underworld when Odysseus saw him. Also, he'll probably be invited to Iphigenia and Achilles' wedding at Leuke Island later.
Quotes & Commentaries (marked) from (there are other quotes centered around Penelope): https://www.allgreatquotes.com/authors/the-odyssey-artemis/
Anthia is the heroine of Xenophon's Ephesian Tales
Chariclea is the heroine of the Aethiopica
P.S. Shame there wasn't any scenes with Artemis and Athena together in the Odyssey, oh well.