It's a puppy and/or newcomer thing, and as Summerleft says, the dogs will work it out themselves. I'd suggest trying not to intervene too much, unless it escalates to "scrapping", in which case if the older dog gets angry enough, the puppy could end up injured. So if things get too rough, I'd just remove the pup from the room 'til everyone's calmed down. My concern would be if you keep pushing puppy away when it nips, it may interpret this as a game (and not stop doing it).
There will be a pecking order, which will be worked out between the dogs themselves.
At one time, we had 3 dogs + 3 cats. The cat which was the first pet introduced into the household firmly established himself as "the boss" at the outset + maintained this standing until he died
And some of the dogs he 'ruled' were BIG dogs.