Yes, Chaucer introduced me to the term. Bungay in Suffolk still has a Town Reeve. Here’s an extract from their website:
The Town Reeve of Bungay is unique in the United Kingdom as the survivor of a Saxon civic authority though there is still an active Portreeve in Laugharen, south-west Wales, and Ashburton in Devon. The earliest surviving record of a Town Reeve in Bungay, William Brooke, appears in the St. Mary’s Churchwardens’ Book in 1536, now in the Suffolk Record Office. A complete series of Town Reeve biographies from 1725 to 1986, compiled from account books, has been published and is on sale in the town.
The Town Reeve today is nominated annually by the predecessor: no voting takes place and the name of the successor is kept secret until the handover of office at a public meeting in December.