Secret hostelry supported by Her Majesty (5)
I believe the answer is:
inner
'secret' is the definition.
(thesaurus)
'hostelry supported by her majesty' is the wordplay.
'hostelry' becomes 'inn' ('inn' can be a synonym of 'hostelry'**).
'supported by' means one lot of letters go next to another (letters go below - in down clue).
'her majesty' becomes 'er' (Elizabeth Regina).
'inn'+'er'='INNER'
(Other definitions for inner that I've seen before include "Located inward" , "Exclusive to a center" , "Nearer to the centre, deeper" , "Area near to bull's-eye" , "(Hit on) part of target immediately next to the bullseye" .)