Den's after odd pieces of each cake (6)
I believe the answer is:
eclair
'cake' is the definition.
(eclair is a type of cake)
'den's after odd pieces of each' is the wordplay.
'den' becomes 'lair' (synonyms).
'after' says to put letters next to each other.
'odd pieces of' indicates alternate letters.
The alternating letters of 'each' are 'ec'.
'lair' put after 'ec' is 'ECLAIR'.
(Other definitions for eclair that I've seen before include "Cake, "long in shape but short in duration"" , "Chocolate-topped, cream-filled cake" , "Lacier (anag.)" , "Soft cream cake" , "Sweet thing" .)