My DS also just started Yr7.
Our routine:
He arrives home approx 4.45 (finishes at 4pm, but likes to get bus with mates, which i consider to be a good social event for him, as the bus journey sounds fun, so I don't urge him to get an earlier bus. he has to have some life too)
Cup of tea and snack. We 'agree' that he will have some free time and then get down to the nasty stuff by 5.30. This allows for one piece of homework to be done.
We eat early, at 6pm. (This can take an hour if we are very naughty and watch a TV while we eat). So say at 7pm he has to go back to it. This will usually be another two pieces.
He has until 8.30 when he has to perform ablutions and go to bed, reading until 9pm, then lights out. Goodnight Vienna.
We have sorted out a homework plan, which bits to do on what days. His homework is set in either 20/30 or 40 minutes parts, with an hour for Art/DT, etc. We have arranged so that the big things like Art/DT/IT are done at the weekend, when he has more time/patience. But weekdays, if he has a 20 minute bit then he also does a 40 minute bit. And on the days when he doesn't get set homework for that subject, I try to persuade him to bring one piece forward.
This includes Saturday and Sunday, even Friday evening.
Last night he realised he had forgotten to bring home his Maths books, so couldn't do homework due in today. Minor panic but we accepted he would get a detention after school for forgetting to take home books/do homework. Then, I looked at timetable and realised he has two break periods and he can go to library to do homework in those periods (NOT ideal, I know, but needs must when the devil drives).
So far we are managing, and he's not fraught or anxious.
So, in short (because I have been lengthy, sorry) he has to realise this is his responsibility. Then (if you haven't already) you need to organise his time (with his input and agreement) to create a 'do-able' rota.
Also, he needs to do it with some breaks, children's concentration is approx 20 minutes.
I strongly recommend some incentive/reward system, so when he manages to do all his set homework for one day he gets some treat, whatever that may be. And at the end of a week in which he has managed it all, another treat.
At (state) primary, my DS was a nightmare about homework. We had loads of silly projects, and I did most of them. Now I realise this can't happen, so i don't correct his homework (hard though this is). It's my job to get him to find the time to do it. It's his teacher's job (plural) to correct it and teach him better for next time.
It's about time management. he can do it but you are going to need to help him in the beginning. Also, It's a huge change and that makes us all tired. Remember how tiring it is when you start a new job? He may not be firing on all cylinders just yet. Also his days are long, up at 6am. Could you get him to bed for 8, then lights out at 8.30?
And I agree, handing in incompleted pieces of work will make him feel anxious in the run up to handing in/getting back, etc, and he needs to do what's set. You will get there, I'm sure. he's probably never had to organise his time before, so you need to show him how.
Good luck.