Private hotel, second in Queen Street (9)
I believe the answer is:
innermost
'private' is the definition.
(thesaurus)
'hotel second in queen street' is the wordplay.
'hotel' becomes 'inn' (inn is a kind of hotel).
'second' becomes 'mo' (both are short periods of time).
'in' is an insertion indicator.
'queen street' becomes 'erst' (I can't explain this - if you can you should give a lot more credence to this answer).
'mo' going inside 'erst' is 'ermost'.
'inn'+'ermost'='INNERMOST'
Can you help me to learn more?
(Other definitions for innermost that I've seen before include "Closest to the centre" , "extremely intimate" , "farthest from border" , "Furthest in" , "nearest the centre" .)