To provide a formal, Irish Times-style headline, here are a few options depending on the specific focus of the article:
Option 1 (Focus on her professional conduct):
“Inquiry opened into conduct of Dr De Brún regarding public health claims”
Option 2 (Focus on the medical regulatory context):
“Dr De Brún to face disciplinary hearing over social media discourse”
Option 3 (Direct and neutral):
“Medical Council to investigate concerns over Dr De Brún’s public statements”
Recommendation:
Option 1 is the most representative of the Irish Times house style for reports involving official regulatory investigations.