Clint Barton takes center stage in Hawkeye. He is one of the less flashy Avengers because he doesn't have super powers per se, so his character typically is in the background and doesn't get as much attention as the other Avengers. However, he clearly had a close relationship with Natasha Romanoff, and with the recent release of Black Widow, it makes sense to make Clint's Hawkeye character the main protagonist in this story.
Clint's actions as Ronin in Avengers: End Game catch up to him in this series. He murdered the father of mafia member Maya/Echo, and she is out for revenge. We're introduced to Kate Bishop, a college archery student and fanboy of Clint. Kate's mother is in debt to mafia ruler Kingpin. Her fiance (Jack) is a sword collector, and Kate stumbles upon a black market auction where Jack buys Ronin's sword. The auction is interrupted by members of the Tracksuit mafia, who is run by Kingpin, looking for an Avengers Rolex watch. Ronin's costume is also up for auction, and Kate puts it on as a disguise to escape the auction and the Tracksuit mafia. The mafia, however, discover her identity and think Kate is Ronin. Clint becomes aware of the situation after seeing a Ronin story on the news, and joins Kate to protect her and calm the situation with Kingpin and the Tracksuit mafia. To complicate matters, Natasha's sister Yelena shows up (as foretold in the credits scene of Black Widow), trying to kill Clint because she believes Clint killed Natasha. All of this occurs in a brisk, 6 episode series that takes place over a week in New York City during Christmas time.
Hailee Steinfeld plays Kate Bishop. She is a person I've heard of before, but prior to Hawkeye I've never seen her in anything or heard her music. I initially found Kate's character a bit annoying, but as the series evolved, so did her character, and as she transformed from fanboy to an actual superhero, I found her less annoying and liked her more. As the series ends, Kate is searching for a superhero nickname for herself, and Clint hints that she could use Hawkeye as her alias. When you read about Kate's character, she is referred to as Hawkeye in the comics, so I get the feeling that we will be seeing more of Kate Bishop as the MCU progresses. Additionally, I hope they put Natasha's sister Yelena in every MCU project moving forward. Florence Pugh nearly stole the show from Scarlett Johansson in Black Widow, and she was fantastic in Hawkeye.
The biggest mystery remaining surrounds the Avenger's Rolex. Apparently it belonged to Clint's wife Laura. But the number on the watch was associated with a different person from Agent Carter, so maybe more to come on this topic and Laura's standing as a SHIELD agent.