Naval Health Clinic Quantico website 1-703-784-1725 or 1-888-784-1802 Monday - Friday: 7:30 a.m. - 6:00 p.m. limited services after 4:00 p.m. Call 1-800-TRICARE, and talk to a nurse who can answer health-related questions (available 24 hours a day 7 days a week)..