Some people are clingy when they get into a relationship. Often times, this is because the person is insecure with themselves and will feel jealous if they don’t know where their significant other is at all times. If you are okay with how clingy your girlfriend is being, then you should continue the relationship.
However, if her clinginess is even the least bit annoying, then you should not continue the relationship. Over time, you are going to feel annoyed by her clinginess. Therefore, you should explain your feelings toward your girlfriend about her clinginess to see if she can change.
Most clingy people can’t just stop being clingy. It will take some time and therapy to make them stop. So don’t expect it to stop immediately.