Pie begins with edges trimmed (4)
I believe the answer is:
tart
'pie' is the definition.
(I know that tart is a type of pie)
'begins with edges trimmed' is the wordplay.
'begins' becomes 'starts' ('start' can be a synonym of 'begin').
'with edges trimmed' indicates the central letters (letters at the edges are removed).
The centre of 'starts' is 'TART'.
(Other definitions for tart that I've seen before include "Acidic in taste" , "Cutting, pastry" , "quiche, perhaps" , "Bitter - pudding" , "Open cake with jam etc" .)