Chris and Liz Walker took over the business in the town centre last Monday but will retain the old name. Appleby's was established in 1895 by John Henry Appleby, a renowned photographer.
In more recent times, his twin grandsons Des and Doug Appleby had run the shop, but when Des died recently, Doug (69) decided it was time to sell.
The Walkers said the shop would continue much in its present style.
The toy department, the gift department and the news agency would all continue, along with fishing equipment and cycle accessories, Mrs Walker said.
Mr Appleby said the shop had traded almost continuously from 1895, apart from being closed for rebuilding for a few weeks after a major fire in 1914.