Move gradually along ridge, letting go of line (4)

I believe the answer is:

edge

I'm a little stuck... Click here to teach me more about this clue!

'move gradually' is the definition.
(to edge along slowly)

I cannot understand how the remainder of the clue works.

(Other definitions for edge that I've seen before include "Force" , "Perimeter" , "Sharpened side of blade" , "Margin, extremity" , "Guitarist with U2" .)

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app