Mr Burrell-Hodgson, 53, has not been seen since 10am on Monday, at his home in Deighton.
Police say they are extremely concerned for his welfare, and are urging members of the public to report any possible sightings.
Mr Burrell-Hodgson is 6ft 1ins tall, has a stubble beard and short dark hair.
He may be driving a grey Land Rover Defender with the registration number PK62 ORA.
Due to the remote, rural location of the Moors, officers have deployed drones and are using off-road police bikes to cover the area.
Inspector Phoebe Southall, of North Yorkshire Police, said: "We are extremely concerned for Gerrard’s welfare, and extensive police searches are continuing today.
"I would urge anyone who may have seen him or his grey Land Rover Defender – particularly east of the River Rye and Hawnby Hill Crag area – to get in touch.
"Please call North Yorkshire Police on 101, quoting reference 12210069596."