Exmoor is not well known as a venue for rock climbing, especially when compared to many of the other National Parks, but opportunities do exist if you know where to go.
The most obvious place to start is The Valley Of Rocks near Lynton. A number of climbs have been established here that span the grades and it is probably the best place for beginners.
For the more experienced climber, there are a number of routes along the costal cliffs. They are adventurous undertakings and not suitable for beginners.
For information about climbing in the Valley of Rocks you may find the UK Climbing site useful.
The beaches of Lynmouth provide a fine area of bouldering that has been developed over the last few years. A downloadable PDF guide has recently been produced and can be found at http://javu.co.uk/Climbing/Guides/index.shtml
A number of outdoor education providers offer opportunities to experience climbing for the first time or to improve your skills. Indoor climbing is also available within easy reach of the National Park. The Active Exmoor website has more details on both activity providers and indoor climbing walls.