Network Rail has announced that the railway between Carlisle and Appleby will be completely closed "for many months" whilst work is being undertaken in the Armathwaite area, where there was a landslip in December. Trains are running between Leeds and Appleby to a revised timetable and a replacement bus service is operating between Appleby and Carlisle. The full statement from Network Rail can be found at http://www.networkrail.co.uk/news/2016/feb/railway-carlisle-appleby-closed-months-landslip/
You are advised to check with Northern Rail tel 0333 222 0125 or www.northernrail.org for further information. The revised timetable is here http://www.northernrail.org/news/7861
See also the Settle - Carlisle Railway web site
http://www.settle-carlisle.co.uk/northern-section-of-line-closed/