Cake some aged shipbuilder left unfinished (5)
I believe the answer is:
genoa
'cake' is the definition.
(I've seen this before)
'some aged shipbuilder left unfinished' is the wordplay.
'some' says to take the centre.
'shipbuilder' becomes 'Noah' (I have seen 'Biblical shipbuilder' mean 'noah' so perhaps 'shipbuilder' could also mean 'noah').
'left unfinished' means to remove the last letter.
The centre of 'aged' is 'ge'.
'noah' with its last letter removed is 'noa'.
'ge'+'noa'='GENOA'
(Other definitions for genoa that I've seen before include "Cake type; foresail" , "Italian city has no age, oddly" , "Italian city; sail" , "City of Italy" , "Type of rich fruit cake" .)