In general ATC is not aware of any RA occurring in aircraft, and is neither aware of the RA content. The crew informs ATC using a phraseology described in ICAO Doc 4444 PANS-ATM, Chapter 12, Para 18.104.22.168:
- When the RA occurs, and the crew must deviate from ATC instructions, they inform ATC with "TCAS RA" when possible.
- If an ATC instruction is received, which contradicts a current RA, they inform ATC with "Unable, TCAS RA".
- The crew then informs ATC when the RA has ended, with "Clear of conflict, returning to (the ATC clearance)", and "resumed" when done.
As @J.Hougaard mentioned, there are some experimentation going on to downlink RA to ATCO display, but nothing mandatory, the information displayed varies and somehow conflict, or introduces a confusion, with ICAO recommendations. So far it seems Czech Republic, Hungary and Japan have a downlink capability. More on Eurocontrol site.
When informed, ATC doesn't provide further instructions to this aircraft before receiving the "clear of conflict" confirmation.
RA always takes precedence on ATC and must be followed by the crew, even if the crew has the intruder in sight and another safe maneuver could be executed as well. The reason is because there is no certainty that the aircraft they have in sight is the conflicting one, or is the only conflicting one.
See instructions to ATC and RTF Phraseology associated with TCAS RAs.
(Indeed a pilot can deviate from anything, but must later demonstrate that they were justified in doing this).