Jeremy Renner’s character Hawkeye was one of the last names to join the Avengers and we cannot exactly say he played an important role for MCU until Avengers: Age of Ultron. That being said it still is not enough for Hawkeye fans.
It is pretty clear that his character will never take the lead or play a significant role in the Avengers franchise. Doctor Strange taking Marvel to the realm of magic and whatnot is also a sign that Marvel is exploring some other ideas. Renner seems like he is pretty okay with the idea of making a Netflix original series for Marvel.
During his interview with IGN to promote his upcoming movie Arrival, Renner was asked about this production idea. Daredevil, Jessica Jones, and Luke Cage are all quality shows which might be great examples for Renner’s Hawkeye and the star just said he would be open for it, if it was brought to him. Here’s his statement:
I don’t know the practicality of that, but any of these characters that I play I’d love to dig into more. I never feel like I get enough time with any character I play, and that’s one of them.