Confirmed Covid-19 cases have risen in the district recently with 24 positive tests over the last ten days.
In comparison, there were 13 confirmed cases in Richmondshire between September 5 and 15.
Cases in other areas of North Yorkshire have been increasingly sharply this month but the rate of new confirmed cases in Richmondshire had not increased significantly until recently.
Official government data shows there have been 328 confirmed cases in the district since the pandemic began.
This chart shows the daily positive tests in the district:
Figures showing localised positive cases show there were six confirmed cases in the Catterick Garrison and Colburn area between September 14 and 20, and four in Richmond over the same period.
Office for National Statistics figures show 51 people have now died after testing positive for the virus, with 412 people passing in the district since the start of the year in total from all causes.
However, there have been no deaths in the district linked to the coronavirus since the week starting July 20.
In his regular bulletin North Yorkshire County Council chief executive Richard Flinton said the second wave had now reached the county.
He said: “The anticipated second wave of coronavirus is with us and seeping into our communities at an unwelcome rate.
“We must all remain in the highest state of alert to prevent it shutting our county down, closing our schools and businesses and taking our freedoms once again.
“In North Yorkshire, we are famous for our straight talking, no nonsense approach to life and our hearty welcome to visitors; for our world famous food and drink, outstanding hospitality offer and inspiring scenery.
With that in mind, I won’t hold back – now is not a moment for stepping around the issue. We must act right now – every one of us – this minute, and every minute to contain it and protect our most frail residents.
“Please speak to your friends, family, neighbours and work colleagues. Encourage them to adhere strictly to the hand washing, face covering and social distancing measures that we all know work. But they only work if we actually do them in a consistent way.”
Mr Flinton warned that a small but growing number of care homes now had residents who are testing positive for Covid-19.
He added: “We are all very aware of the cruel nature of Covid and how it targets vulnerable people without pity.
“Let’s pull together and protect them, protect our freedom, protect our businesses and protect our future together.”