Splinters an organ in the ship (7)
I believe the answer is:
slivers
'splinters' is the definition.
(I know this)
'an organ in the ship' is the wordplay.
'an organ' becomes 'liver' (liver is a kind of organ).
'in the' indicates putting letters inside.
'ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'liver' going inside 'ss' is 'SLIVERS'.
(Other definitions for slivers that I've seen before include "Thin strips of wood or glass" , "Bits" .)