American forces let out of living quarters for the ship's crew (10)
I believe the answer is:
forecastle
'living quarters for the ship's crew' is the definition.
(area on a ship containing crew's quarters)
'american forces let out' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'a'+'forces'+'let'='aforceslet'
'aforceslet' anagrammed gives 'FORECASTLE'.
'of' acts as a link.
(Other definitions for forecastle that I've seen before include "located at the front" , "section of the ship" , "Part of vessel" , "Where the crew may be" , "Forward under-deck part of a ship" .)