NHS Test and Trace will be working with the local authority to increase testing in Wakefield North, Wakefield South, Wakefield East, Pontefract North and Pontefract South, with all adults who live and work in the areas being asked to get tested.
There will also be enhanced contact tracing used for anyone testing positive for a variant of concern - this is where tracers look back over an extended period to determine the route of transmission.
The case rate for Wakefield is 87 per 100,000, which is just above the national average of 63 per 100,000, according to the latest government data. There have been no deaths because of Covid-19 in the city for four weeks.
Cllr Denise Jeffery, Leader of Wakefield Council, said: "Everyone is wanting the remaining restrictions to be lifted so we can continue moving forwards to a normal way of life.
"Increasing our testing offer will help us to take the next step to a more familiar future and I urge everyone to play their part by taking part in testing, having their vaccine and following the latest guidance."
People are able to book a test online or by calling 119 - people can choose to go to a testing site or to have a test sent to their home.
Wakefield's Director of Public Health tells ITV News hospital admissions and deaths remain low
Anna Hartley, Wakefield Council’s Director of Public Health, said: "Cases of the COVID-19 Delta variant continue to rise across the Wakefield district. We are actively monitoring the situation and taking all necessary action.
"We are increasing testing capacity and continuing to promote vaccination in areas experiencing cases of the Delta variant through proactive measures including community door knocking."
The MP for Normanton, Pontefract and Castleford, Yvette Cooper, said: "We've been calling for some weeks for more testing and faster vaccinations in the district so that we can try and get ahead of this and so that we can make sure that we don't go backwards again, which I don't think anybody wants."
People are being urged to follow government guidance on mask-wearing, hand washing, social distancing and self-isolation.