The 47-year-old mother-of-three was killed in a knife attack at the Hall Lane property on Friday evening and her body was discovered the following day.
Police are now questioning the suspect in connection with the incident and he remains in custody.
It follows the release of CCTV footage showing a man cycling in the village and then outside the house on foot where the murder took place.
Assistant Chief Constable Rob Griffin, of Nottinghamshire Police, said: “This arrest follows public appeals for information that we have made over the last few days.
“However, I would ask that people keep providing information as this investigation continues.
“Every piece of information we receive helps us get closer to an understanding of the events of that night.”
ACC Griffin said the investigation was progressing well with detectives working round the clock to follow up every lead, and he praised the public for coming forward with information that has helped the investigation.
He urged anyone with further information, or CCTV or dashcam footage in and around the area on that night, to come forward.
“I want to thank the public once again for their support for this investigation and all the information they have given us so far,” he said.
“I am fully aware how shocking this incident has been for Clair’s family and the wider community in Colston Bassett, which is why we have invested so much resource not only in the investigation itself but in providing a uniform presence in the area to give people reassurance.”
Anyone with information is urged to call 101, quoting a new incident number, 277 of March 3, 2022, or Crimestoppers anonymously on 0800 555 111. People can also report information at https://mipp.police.uk/operation/33EM22E38-PO1 through an online portal.