On the Dalek Foundation world of Carthedia, skimmers were used as flying police cars. When the Eleventh Doctor rescued Sabel, Jenibeth and Ollus Blakely from an orphanage, they escaped in a skimmer. Hellic Dansard and other police officers pursued them in other skimmers but the Doctor was able to use holograms to make a Dalek think it was under attack, causing it to panic and accidentally shoot the other skimmers out of the sky.
Drax owned a "home-made" skimmer on Gallifrey, which he used to travel to his House with instead of staying at the Prydonian Academy dormitories. He would often give Jelpax a lift home. (PROSE: Divided Loyalties)
During the time of Romana II, skimmers still existed on Gallifrey, but were considered archaic technology, and hence were long out of use, at least by those who lived in the Capitol. (AUDIO: Fractures)