Problem that is hampering American warship's return (5)
I believe the answer is:
issue
'problem' is the definition.
(thesaurus)
'that is hampering american warship's return' is the wordplay.
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'hampering' indicates putting letters inside (hamper can mean to obstruct or restrain).
'american warship' becomes 'uss' (naval abbreviation for United States Ship).
'return' shows that the letters should be reversed in order.
'uss' written backwards gives 'ssu'.
'ie' enclosing 'ssu' is 'ISSUE'.
(Other definitions for issue that I've seen before include "Question in dispute to be settled" , "Topic (to be addressed)" , "Matter, point" , "Subject of debate" , "Children; important topic" .)