Sudden movement doesn't finish an organ (4)
I believe the answer is:
lung
'an organ' is the definition.
(I know that Lung is a type of organ)
'sudden movement doesn't finish' is the wordplay.
'sudden movement' becomes 'lunge' (I've seen this in another clue).
'doesn't finish' means to remove the last letter.
'lunge' with its last letter removed is 'LUNG'.
(Other definitions for lung that I've seen before include "urban area" , "Respiratory organ" , "breather" , "One of a pair of organs in the ribcage" , "Organ used for breathing" .)