Diligent American pursues one couple behind a ship (9)
I believe the answer is:
assiduous
'diligent' is the definition.
(similar in meaning)
'american pursues one couple behind a ship' is the wordplay.
'american' becomes 'US' (United States).
'pursues' is a charade indicator (letters next to each other).
'one couple' becomes 'duo' (two people).
'behind' means one lot of letters go next to another.
'a ship' becomes 'assi' (I am not sure about this - if you are sure you should believe this answer much more).
'duo' after 'assi' is 'assiduo'.
'us' after 'assiduo' is 'ASSIDUOUS'.
Can you help me to learn more?
(Other definitions for assiduous that I've seen before include "Diligent" , "Marked by care and persistent effort" , "Hard-working" , "Persevering" , "Showing great care and perseverance" .)