Little mite smuggled aboard ship doesn't go away (6)
I believe the answer is:
sticks
'doesn't go away' is the definition.
(to stick somewhere is to remain there)
'little mite smuggled aboard ship' is the wordplay.
'little mite' becomes 'tick' (parasitic creature).
'smuggled aboard' is an insertion indicator (I've seen this in other clues).
'ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'tick' put within 'ss' is 'STICKS'.
(Other definitions for sticks that I've seen before include "Stands" , "Glues" , "''... and stones may break my bones but names will never hurt me''" , "Small pieces of wood" , "Old fogeys" .)