Proprietor to make an admission with some hesitation (5)
I believe the answer is:
owner
'proprietor' is the definition.
(I know that proprietor can be written as owner)
'an admission with some hesitation' is the wordplay.
'an admission with' becomes 'own' (I can't justify this - if you can you should give a lot more credence to this answer).
'some hesitation' becomes 'er' (sound used when hesitating).
'own'+'er'='OWNER'
'to make' is the link.
Can you help me to learn more?
(Other definitions for owner that I've seen before include "The one in lawful possession" , "Title-holder" , "Title holder?" , "Keeper" , "One who possesses" .)