How to stop 3 year old from being mean to 1 year old

When I first had my youngest daughter my oldest would hold her and help out. Now that my youngest is 1 my 3 year old has become extremely mean. She snatches toys from her and sometimes even hits. I absolutely do not tolerate this behavior, she gets a time out every time I witness her hitting. I’m starting to feel my oldest daughters behavior has negatively impacted my 1 year old. My youngest has become extremely clingy and she doesn’t want to play alone without me anymore. Idk if my one year old is just going through a phase or if my oldest daughters behavior is really bothering her. Any advice?