Culinary herb in sink, last of thyme (4)
I believe the answer is:
sage
'culinary herb' is the definition.
(I've seen this before)
'sink last of thyme' is the wordplay.
'sink' becomes 'sag' (sagging is a kind of sinking).
'last of' indicates one should take the final letters.
The final letter of 'thyme' is 'e'.
'sag'+'e'='SAGE'
'in' acts as a link.
(Other definitions for sage that I've seen before include "A herb or a guru" , "Wise woman" , "Clary" , "Clever" , "Velvety-leaved herb" .)