If a tile has slipped or shifted from its position then it can be difficult to remove due to the retaining nibs on their back edges. Use wooden battens to lift the two overlapping tiles immediately above the tile you need to replace.
Next try lifting the tile in order to allow the nibs to clear the batten and then pull it out. If this fails, the tile could be nailed into position. Try rocking the tile from side to side to loosen the nails. If it still refuses to move use a slate ripper.
A slate ripper is a flat tool with cutting barbs at one end. Slip a slate ripper under the centre of the tile. This will enable you to locate the hooked end over the fixing nail. The steel blade slips under the tile until one of the barbs of the arrow shaped tip hooks round the nail that is driven into the roof batten.
Once engaged, pull out the nail by pulling down on the tool or giving a hammer blow on the curved handle. If the nail is proving difficult, the tool will cut through the nail. Repeat the procedure with the second fixing nail and remove.
It may be necessary to remove both fixing nails before slipping the tile back into position. Slate rippers can be hired, check out the prices before purchasing the tool.