Aircraft performance should normally suffice to execute the TCAS RA in which case you are required to do so. If you can't fully comply with the RA, get as close to it as you can whilst protecting the stall envelope. This applies even if it means acting against your ATC clearance.

In case of any conflict between TCAS, ATC and stall warning, follow:

 1. stall warning
 2. [GPWS][1]
 3. [TCAS][2]
 4. [ATC][3]

In that order of priority.


  [1]: https://en.wikipedia.org/wiki/Ground_proximity_warning_system
  [2]: https://en.wikipedia.org/wiki/Traffic_collision_avoidance_system
  [3]: https://en.wikipedia.org/wiki/ATC