Complex sentence: Many of the mines are owned by the National Trust and have been leased from them by the Derbyshire Caving Club that maintains access and continues to explore and search for areas of mining that have been closed for centuries.
Split into simpler sentences: Many of the mines are owned by the National Trust. The Derbyshire Caving Club have leased the access rights, and they continue to explore and search for areas of mining that have been closed for centuries.