Clinginess is due to fear of being abandonment and rejection. It also has to do with a sense of inferiority and insecurity. It suggests that you lack confidence and are too needy. You need to find a way to feel valuable and whole. There may be a basis for your fear if you feel that your partner is not trustworthy and faithful, so that is also something you should investigate. If he is faithful, you need to be brave enough to give him space to be himself and spend time with other people without smothering him or he will rebel.
I completely agree with Angie. The way to stop being clingy is to do activities on your own that only you enjoy and encourage him to do the same. It's good for couples to have time apart. It makes their time together all the more enjoyable. Plan a girls' night out or spend a quiet evening at home by yourself.
It would be a good idea for you to focus on yourself for a while. Figure out what it is that you like to do when you’re not with him. What are your hobbies? What are your talents? I would also suggest spending some time volunteering. This will take your mind off of your boyfriend and you will also accomplish something useful in the process.
Clinginess can result from several sources, and usually is due to a mix of factors. Girls who hold on too tightly often suffer from low self-esteem and fear of abandonment. It’s important to determine whether those fears are grounded in the current reality or something experienced in the past, with the father or another male figure. When you can see that your boyfriend does value and appreciate you, wants to be with you and isn’t looking for someone else, it’s easier to let go. Also, girls who spend time pursuing their own interests and hanging out with their friends are less likely to cling to their boyfriends.