WASHINGTON, Sept 27 (Reuters) - Federal Reserve Governor Lael Brainard said Monday the U.S. had fallen behind its peer central banks in building the risks of climate change into the supervision of banks, highlighting a potentially core priority should she be promoted to vice chair of supervision at the Fed or even to the chair"s spot. "A lot of our largest banks who are internationally active are already being supervised in other jurisdictions to make sure they are measuring, monitoring and managing climate related financial risks," Brainard said in comments at a National Association for Business Economics conference. "The U.S. has been behind and we need to catch up...The nature of climate change is such that...it could pose significant risks both in terms of sudden changes in asset prices but also change the financial system generally."