One way that is effective at dealing with a clingy baby is to stay close, but have others engage your baby in play. Once your baby is happily playing with someone else, you can leave and know that your baby is perfectly content. You may not want to leave the first couple of times your baby is playing with someone else. If you are close by, your baby will feel safe exploring and interacting with others and will gradually feel like they don’t have to cling to you.
Another way to handle a clingy baby is to have your spouse take over a specific baby routine, such as bath time or getting dressed or reading a story before bed. Your baby will enjoy this time with your significant other without you and you can have a moment to yourself. Know that you may have to deal with a little bit of fussing when you first start this routine, but it will be short lived.
In general, keep in mind that having a clingy baby is only a stage and it will soon pass.