Almost spill over edges (4)
I believe the answer is:
lips
'edges' is the definition.
(lip is a kind of edge)
'almost spill over' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'over' is a reversal indicator.
'spill' with its final letter taken off is 'spil'.
'spil' written backwards gives 'LIPS'.
(Other definitions for lips that I've seen before include "Fleshy folds of tissue" , "Take, O take those - away (Measure for Measure)" , "margins" , "Fleshy folds on the face" , "What form the opening to the mouth" .)