New NSW Police Commissioner Mick Fuller has removed Deputy Police Commissioner Catherine Burn from responsibility for counter terrorism, handing the key responsibility to her colleague, Dave Hudson.

Ms Burn, who earlier this month was overlooked as the successor to then-commissioner Andrew Scipione, had been deputy commissioner for specialist command, which has responsibility for counter-terrorism, since 2012.

She has now been given the position of Deputy Commissioner for Specialist Support.

Mr Hudson, the deputy commissioner overseeing corporate services since 2013, will become Deputy Commissioner for Investigations and Counter Terrorism.