TCAS II provides the pilot with specific instructions on how to avoid the conflict with traffic. These instructions are known as a “Resolution Advisory” (RA) and may instruct the pilot to descend, climb, or adjust vertical speed. TCAS II systems are also able to communicate with each other to ensure that the RA provided to each aircraft maximizes separation.
From https://nbaa.org/aircraft-operations/communications-navigati...
My understanding is these automated instructions override those from ATC