HHS Secretary Alex Azar tapped John O’Brien to become the new department’s “drug czar” Dec. 6, a sign Azar is looking for consistency within the agency after a former drug adviser’s death.

O’Brien has held multiple positions within the Health and Human Services Department, including advisor to the secretary for health reform and drug pricing and deputy assistant secretary for heath policy.

Now O’Brien will head up the agency’s efforts to lower drug prices, a high profile position given the...