Classified hotels accommodating American more than once (4-4)
I believe the answer is:
'classified' is the definition.
'hotels accommodating american more than once' is the wordplay.
'hotels' becomes 'HH' (two H's - hotel is H in the NATO phonetic alphabet).
'accommodating' means one lot of letters goes inside another.
'american' becomes 'US' (abbreviation for United States).
'more than once' shows that letters should be duplicated.
'hh' placed around 'us' is 'hush'.
'hush' duplicated is 'HUSH-HUSH'.
(Other definitions for hush-hush that I've seen before include "Clandestine" , "Informally kept very secret - twice?" , "Highly confidential" , "Highly secret" , "Cloak-and-dagger, secret" .)