Unproductive anger after ship’s back without navy (7)
I believe the answer is:
sterile
'unproductive' is the definition.
(unable to reproduce)
'anger after ship's back without navy' is the wordplay.
'anger' becomes 'rile' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'ship's back' becomes 'stern'.
'without' suggests deleting specific letters.
'navy' becomes 'RN' (abbreviation for Royal Navy).
'stern' with 'rn' removed is 'ste'.
'rile' after 'ste' is 'STERILE'.
(Other definitions for sterile that I've seen before include "Aseptic or infertile" , "Germ-free" , "Like theatre" , "Fruitless" , "like a mule" .)