It depends. To claim after-school expenses, the child or dependent must be age 13 or younger. You must be the custodial parent. . All expenses must be incurred so that you could work, look for a job or go to school full-time. If you are married, your spouse must also meet the same work requirements.
Although divorced parents may alternate claiming children as dependents, this credit is strictly reserved for the custodial parent.
My child is a competitive gymnast, under age 13. She attends gymnasts 14 hours a week. I’m divorced, filing as head of household. I claim child as dependent for tax purposes. I work part time and only occasionally work when she is in gymnastics. I am there watching most of the time. Can I claim an after school care tax deduction? Please explain why or why not.
You wrote:
"I work part time and only occasionally work when she is in gymnastics. I am there watching most of the time."
The child care credit is a credit people get when they pay for child care so they can work. Why would you expect a credit for time when you are sitting in the same place with your child while the child takes a gymnastics class? The child care credit was not intended as a method of subsidizing your child's extra curricular activities.
https://ttlc.intuit.com/questions/1900643-what-is-the-child-and-dependent-care-credit