Hurried to consume last of sweet cake (5)
I believe the answer is:
torte
'sweet cake' is the definition.
(I've seen this before)
'hurried to consume last' is the wordplay.
'hurried' becomes 'tore' (tearing is a kind of hurrying**).
'to consume' is an insertion indicator.
'last' becomes 't' (I've seen this in other clues).
'tore' enclosing 't' is 'TORTE'.
'of' is the link.
(Other definitions for torte that I've seen before include "Sweet cake or tart" , "Rich (Austrian) cake or pastry" , "1d [PASTRY]" , "German cream cake" , "Sweet cake (from Ger.)" .)