“What can I do for my child's separation anxiety?”

Depending on child's age, some degree of separation anxiety can be a normal part of developmental process (typically in younger children). However, if you are feeling these behaviors are outside of typical developmental age range and has been ongoing - I would recommend consulting first with pediatrician to discuss and if needed look for therapeutic services for yourself and/or child. There are techniques and therapeutic interventions that can assist. It is hard to give more concrete guidance without specifics.

Good morning and thank you for the question. Without knowing the age of your child, some separation anxiety is normal and age appropriate; however, if it escalates to the point where, as you mentioned, it becomes a challenge to leave for work or even the room, then there are some things you can do to reassure your child. If your child is school-aged and going off to school, never linger; and the same goes for when you are leaving for work. Tell them, "Mommy will see you later. Love you and have a good day." When you all reconvene tell them I am so glad you had a good and see Mommy did come back just like I told you. It is important to reassure and keep so-longs to a minimum when leaving.
I hope this helps. Warmest regards.