Star Trek: Discovery has introduced many fascinating characters since its first episode, but the show is missing a key Star Trek element: the inclusion of a non-Human character with a desire to attain humanity. The tradition of such a character arguably began in Star Trek: The Original Series with the character of Spock. As first officer to Captain Kirk, Spock provided a grounding of logic and reason to Kirk's more impulsive side, but also captivated audiences' attention in regards to his struggle with his dual nature. Born half-human, half-Vulcan, Spock was constantly at war with himself over which side to listen to. While he was sometimes repulsed by humanity, he was more often fascinated by it and began to act and think more human as his story progressed.
While Spock was dragged only reluctantly towards his more human side, the idea of a character with genuine aspirations for humanity was more fully explored on subsequent shows in the franchise. The character of Data from Star Trek: The Next Generation is perhaps the best example of this; no other character (save perhaps Pinocchio, who Data admired) is better remembered for their quest to become human. On Star Trek: Deep Space Nine, the mantel was picked up by Odo and further explored on Star Trek: Voyager through both The Doctor and later Seven of Nine. The idea of a non-human character who strives to be more than they are is something the Star Trek franchise has become known for doing well mostly because of these characters.
It is surprising then that Star Trek: Discovery had yet to include a character who shares this desire. The only characters who have come close are Saru and Emperor Georgiou, but neither character has displayed the same drive for humanity as characters like Data or the Doctor. Saru is Kelpien, and very proudly so. While he clearly has a great deal of respect and admiration for humanity, his storylines have tended to revolve around his own species and culture. Emperor Georgiou is a Terran from the Mirror Universe, which makes her definition of humanity different than the norm. Although she learned to embrace more aspects of the good side of humanity during her time onboard Discovery, Georgiou continued to retain most of her Terran ideals, and never expressed outright interest in changing her ways to become more like her Prime Universe counterpart.
Perhaps the reason Star Trek: Discovery does not have a character that fits the bill is because they have not yet introduced a character who is a truly unique, non-Human entity. This is something all of the other characters who have strived for humanity have in common. Data was an android, the Doctor a hologram, and for a long time, Odo thought he was the only one of his kind. Even Spock was unique in his hybrid parentage, and Seven of Nine was one of the first former Borg to reclaimed her individuality. Discovery has had no android, hologram, or alien characters who have needed to cling to the idea of becoming human because they have no other role model to base their identity upon.
If Star Trek: Discovery wanted to join the Star Trek tradition of having such a character in the main cast, however, they have an excellent opportunity to do in season 4. The show's time jump to the 32nd century has opened up new avenues within the Star Trek universe that Discovery did not previously have access to, and the possibility for exploration of new alien races or even holographic or android characters had increased dramatically. Introducing a character that wants to be human would provide fans with someone they could invest in more fully, as they have been able to in the past with other shows in the franchise. It would also give Star Trek: Discovery a fascinating storyline to explore in season 4.