I agree with Clark, the most effective way to stop a bird from biting in-general, regardless of the cause, is the "Shunning Method"...If you do a search here you'll find several posts with long, detailed explanations and step-by-step instructions on how to do the "Shunning Method", but basically every time the bird bites anyone (every single time it has to be done or it won't be effective), you tell the bird "No Bites!" (not yelling or scolding, just firmly) and you put the bird right down on the floor for 5 minutes, and everyone in the room as to turn their backs to the bird for the full 5 minutes, and if the bird crawls up you leg, walks around to the face you or anyone else, or if they fly from the floor, you just silently, without saying a word, go get the bird and put it right back down on the floor and again turn your backs to them and totally and completely ignore them for a full 5 minutes...And when the 5 minutes is over you just all walk away and go about your business, and let the bird come to you, you don't immediately go to them...You might have to do this a bunch of times in a row the first day you start it, but if you stick to it and do it every single time they bite anyone, they typically get the point and stop the biting for the most-part in a few days to a week...
Birds absolutely HATE being on the floor because they are the lowest thing in the room and they lose all sense of dominance while on the floor, and by completely "Shunning" the bird and literally turning your backs to the bird, you're taking-away the thing that they crave the most, interaction with their "flock" and attention...
It probably is due to hormones, especially if he is just a year old, that's about the time most Green Cheeks go through puberty...One thing to make sure of is that you Green Cheek has NO access to any small, dark, warm places at all, as them being able to get into/underneath any spaces that are small and dark (simulated nests) causes their hormones to go crazy and this is a very common cause of violent-aggression in a hormonal bird, especially all species of Conures, who are especially effected by small,
dark, warm places...
*****So if your Green Cheek happens to have ANY type of tent, hammock, "Hut" such as a "Happy Hut" or a "Snuggle Hut", or any type of box (wooden, cardboard, etc.) inside of it's cage or anywhere else it might have access to it, or any type of towels, blankets, fabric, cloth, etc. that it can get underneath or make a nest out of, or any type of "bedding" material in it's cage like wood-chips, shredded paper bedding, etc., all of this stuff needs to be removed immediately and kept away from them permanently, because it is no doubt a main-cause of it's aggression and biting. Also, if they have access to getting underneath any furniture in your home, like under the couch, chairs, desks, etc., that needs to be made "off-limits" from now on too...
Just an FYI, if your bird does happen to have any type of "Snuggle Hut" or "Happy Hut", or other type of fabric tent, hammock, or "Hut", not only are they a main cause of hormonal aggression, chronic masturbation and egg-laying, etc., they are also extremely dangerous and potentially life-threatening to you bird, and have directly resulted in the sudden, early deaths of thousands and thousands of pet birds; specifically Conures are prone to dying due to these "Huts" because they so love getting into/underneath small, dark, warm places...They either hang themselves from loose-threads that come-out of the fabric, or more-often they chew-off little, tiny pieces of the material, bit-by-bit, over-time so you don't even notice they are doing it, until one day they are found dead in their cages due to the material accumulating in their Crops, Stomachs, and Intestinal Tracts over-time, finally causing a complete obstruction/blockage which is fatal...Just an FYI, I don't know if your bird has any type of tent or "Hut" at all, but just in-case..