Mr Clark, who was in his 50s, died suddenly in September last year when he was trampled by cows while walking his dogs in a field near the town.
The married father was a keen cyclist and rugby coach and originally taught PE at the school when he joined in 1997.
In memory of Mr Clark, who was also a lover of the great outdoors, the fitness challenge aims to motivate students and staff to collective clock up 8,000 miles walking and cycling this month.
The heart-felt tribute was set-up by Jack Moore and Helen Southgate, current PE teachers at the community comprehensive on the edge of the Yorkshire Dales.
Mr Moore said: "We tragically lost the legend that was Dave Clark... And we have waited to pay our respects as a PE Department with a challenge that he would be proud of.
"Dave was someone who always encouraged students to be the best they could be and always to challenge ourselves."
The target of 8,000 miles is significant as it is the area covered by the Great North Air Ambulance Service and 50 per cent of the money raised will be donated to the charity, with the other 50 per cent to refurbish the school’s fitness room with inclusive equipment.
"We believe that combining our efforts to support the Great North Air Ambulance and also enhance the sporting facilities at Richmond School would be something that Dave would approve of," Mr Moore said.
Sophie Bendelow, a community fundraising officer at the Great North Air Ambulance, added: "We know Dave Clark was a keen sportsman and had previously taught PE so we think it’s lovely that the proceeds will be split between the Great North Air Ambulance Service and getting some new fitness equipment for the school.
"We would just like to say a massive thank you to everyone who is taking part in the challenge and we wish them the best of luck covering 8,000 miles."
The challenge was also inspired by Will Arnold, a Year 11 student, who did his own walk, cycle and running challenge in October last year, raising more than £1,300 for the Great North Air Ambulance.
Ms Southgate said: "We were so impressed with Will’s amazing efforts that we are taking it a step further with a target of covering 8,000 miles."
She added: "We know that we can rely on Team Richmond School to step up to the mark and make this challenge a huge success."
It is hoped that the March miles challenge will also provide a new incentive and drive to get the school community moving again.
"With spring around the corner and some hope on the horizon, and with lockdown measures gradually easing, we feel this is just what we all need to get ourselves re- energised while doing something really positive for our community," said Ms Southgate.
The refurbishment of the school’s fitness room will see it made accessible. This includes equipment suitable for wheelchair users or students and staff who may have health complications that mean they are not able to use some of the traditional fitness kit.
Headteacher Jenna Potter added: "We have been genuinely challenged and deeply saddened by the loss of Mr Clark, who was such an important part of our staff team.
"I hope this challenge is something Dave would be proud of."
Mrs Potter added: "This is a great initiative to get our school community outside and active whilst also doing something extremely positive for our school and the Great North Air Ambulance.
"There will be some friendly rivalry between tutor groups and year groups, with a league table to see who covers the most miles... So let the competition begin!”
You can donate to the March Mile challenge here.
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