Our new 4 month old kitten will NOT stop bullying our 6 year old cat

Hello, we adopted a new kitten 2 months ago from the shelter (both cats are female) the kitten is constantly jumping and biting our sweet and loving 6 year old cat and it stresses her and everyone else out. The kitten will snuggle with us humans but darts straight for our cat and chases her around. I know kittens are capable of snuggling with older cats but this one just doesn’t. I’m afraid we might need to find her another home, because I don’t want our senior cat to live like this forever.