Promoting Lifelong Activity for Youth Act of 2023 or the PLAY Act of 2023 This bill modifies the child and dependent care tax credit to cover expenses for youth physical activities. Such expenses include registration costs, fees, and expenses for the participation of taxpayer dependents between the ages of 4 and 18 years in fitness facilities and physical exercise or activity instruction. The bill also increases the maximum dollar amount for dependent care flexible spending arrangements. The bill directs the Department of Health and Human Services to award grants to promote participation in recreational youth sports.