Buy them stuff - as HoD, you'll be budget holder so set aside some money for this key group and buy them some resources. Get them clear pencil cases, biros, highlighters, maybe some of those thin colourful annotating pens (stadtler triplus or the Sainsburys equivalent at half the price). If they might need to resit language, but them the Pearson revision guides and workbooks. Explain clearly that you see this as an investment in their success and that you expect them to look after it all v carefully. Keep all the packs in school so you never have conflict over arriving ill-equipped. New exercise books with a big emphasis on keeping them as a portfolio of work that shows progress and in good nick. Make sure your classroom is well equipped eg with glue sticks, scissors etc for sticking in worksheets. Make sure all worksheets are pre-trimmed so they can be stuck in neatly with no bother. Basically, make it am absolute expectation that they take pride in their work and make it as easy as possible for them to do it.
If you are studying lit, the short stories are working brilliantly with my C/D borderliners. I'll be happy to send you some resources if you want to pm me an email address. I started Insp Calls but I don't love it and the kids loathed it so for the first time ever I abandoned a text and started again with surprisingly happy results. Character and Voice poems are brilliant for this sort of group, too.
Have you got a visualiser in the classroom? If not, it's really worth getting one for the afl opportunities - you can just stick the exercise book of anyone who has done well and mark it in front of the class for exactly what they've done right. It can be really motivating, especially as you can just cover the rest of their work with a bit of paper and only show the best bit.
Try WAGOLL bingo - get them to make a bingo grid for six success criteria and write in six features they'd expect to see in a good piece of work for whatever skill (WAGOLL stands for what a good one looks like) and then play bingo as you display either a modelled piece or one of their pieces. If they get a line or a full house, they have to be able to explain why the piece on show meets their success criteria. This is doable in 10-15 mins and is good fun.
Set short homeworks and mark them by turnaround so that they get into the habit of doing the work and having it checked straightaway.
I guess it all depends on the culture of the school you're going into and their recent experiences, but if you make them feel secure that you care about the quality of what they do every time they set pen to paper you should get them on side fairly quickly, especially if you can help them to see where they are making progress over a short period of time.
Good luck - it's a tough ask to turn a group around at this stage in the year. They might be quite angry about their last teacher leaving them in the lurch so they might need a lot of reassurance. I'm sure you will sort them out in short order.