Almost broke surface (4)
I believe the answer is:
skin
'surface' is the definition.
(skin is a kind of surface)
'almost broke' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'broke' becomes 'skint' (I've seen this before).
'skint' with its final letter taken off is 'SKIN'.
(Other definitions for skin that I've seen before include "Outer surface" , "Outer covering" , "coat" , "Fell" , "Protective body covering" .)