Kitten constantly meowing and stressing out older cat.

I have a 4 month old kitten and he’s been living with us for a couple weeks now. Introductions with all animals were great. We have 2 big dogs and an elder cat (10) and they all get along. While the kitten and the cat aren’t super close, they’re civil and sleep in the same room. Although every night at around 11 and every morning around 6 the kitten cries non-stop. He will eventually calm down and come sleep and we play during the day. This meowing stresses me and my senior cat out. The elder cat is not aggressive and doesn’t ever fight but will start hissing after a certain point. I don’t know what to do to ensure both of them are happy and also keep me sane.

Hello - you mentioned that the kitten is a boy.  Even so, I think it may be worth saying (just in case) that female cats can come into season at this age and sometimes even in winter, so it's certainly worth double-checking that that's not the case.

I wonder what the kitten is trying to achieve by meowing?  Are they cold, bored or hungry (kittens often need feeding more frequently than other cats), or possibly in need of a way to wear off energy?  Might they be being disturbed by e.g. unseen rats and mice in the walls?  This is a 'thing' in some houses.

To help with cat: cat relations in households, it is helpful if all cats have their own litter tray or access to the outdoors from their own 'territory' within the house (cats do tend to have different territories within a household).  The same goes for access to food;  frequently, cats have to walk across another cats' territory to eat, which can make things difficult.  A chat to your vet who can take a good behavioural history may be very useful now, while it is still early days.  The iCatCare website, run by Sarah Caney who writes for this site (have a look in our blog, too) may turn out to be a useful resource.