Laminator_X
Once & Future KMC Hawkeye
OK, I've just finished reading the EXHAUSTIVE Hawkman mega-bio (which also reminded me why I don't read very much DC) over at monitorduty.
Current Hawkman certainly overmatches Clint physically, but that's hardly ever stopped him from taking people down before (She-Hulk, Abomination, etc), nor does he usually have trouble with fast fliers (other than Kree jetpacks).
Hawkman could draw this by just flying away, but if he's going on the offensive he won't be close to the speed of sound. Unless I'm mistaken, he seems to have a highish max-speed, but not hyper-reflexes like Superman or whomever. He's agile enough for some good dodging, but as usual Hawkeye doesn't need a direct hit to take him out.
The Antarctic Vibranium arrow he used to take out Alkhema would send a suddenly-normal-human Carter dropping to like a stone as his harness dissolves, but in fairness that's a prepped attack.