Subchapter 9.4 – TCAS Resolution Advisory and Safety Alerts

Why TCAS overrides ATC:
Imagine ATC has cleared you to maintain Flight Level 120, and another aircraft is assigned Flight Level 120 from below but has not reached it yet. On radar, ATC is tracking both aircraft, but there is a processing delay or a radar blind spot. TCAS, with its own radar, detects the conflict in real time and commands you to climb. You do so. ATC will see your altitude change on radar, call you, and you explain the RA. This is not a violation; it is safety protocol.
This is why it is absolutely critical that you declare an RA to ATC immediately after the maneuver. ATC uses your declaration to update their picture and to alert the other aircraft of the conflict.