It seems that you have a dominance situation on your hands. It could be playful, but that is something that would have to be determined in person. I worry about leaving them alone together all day. If the older dog is so dominant that it's willing to behave this way in front of you... it's probably worse when you are not around. Obtaining dogs at different times results in this quite often, it's partially a jealousy thing. However, normally spending a lot of time with both dogs equally can put an end to it. When the dog acts this way around you, put a stop to it immediately. In most cases the other dog should stop the behavior when it gets out of hand, but it doesn't seem like your female is doing that herself.
Don't just get him in trouble for being aggressive. Stop the behaviour by saying no firmly, then petting and playing with both dogs for a minute or two. You don't want to associate
trouble with the new dog. If it continues, seek "couples" training from a professional

in person a trainer can help build a friendly bond between the dogs.