Private lodging provided with hesitation (5)
I believe the answer is:
inner
'private' is the definition.
(as in one's private or inner thoughts)
'lodging provided with hesitation' is the wordplay.
'lodging' becomes 'inn' (I've seen this in another clue).
'provided with' says to put letters next to each other.
'hesitation' becomes 'er' (sound used when hesitating).
'inn'+'er'='INNER'
(Other definitions for inner that I've seen before include "Located or occurring closer to a centre" , "(Hit on) part of target immediately next to the bullseye" , "Target next to bull" , "Target zone" , "Bull's penned in by this" .)