Private hotel used by monarch (5)
I believe the answer is:
inner
'private' is the definition.
(thesaurus)
'hotel used by monarch' is the wordplay.
'hotel' becomes 'inn' (inn is a kind of hotel**).
'used by' means one lot of letters go next to another.
'monarch' becomes 'er' (abbreviation for Elizabeth Regina).
'inn'+'er'='INNER'
(Other definitions for inner that I've seen before include "Close to the centre; mental" , "Essential - most private" , "Situated inside" , "Interior" , "closer than magpie" .)