Private agent set up new salon (8)
I believe the answer is:
Here is my best explanation:
'private' is the definition.
('personal' can be similar in meaning to 'private')
'agent set up new salon' is the subsidiary indication.
'agent' becomes 'rep' (short for representative).
'set up' says the letters should be written in reverse.
'new' indicates anagramming the letters.
'rep' in reverse letter order is 'per'.
'salon' is an anagram of 'sonal'.
(Other definitions for personal that I've seen before include "Concerning private life", "Confidential", "Concerning oneself", "Belonging to an individual", "Own", "Of one's private life - nobody else's business", "Such a rude remark", "Of one individual", "Private - bodily" and "Intimate - in the flesh".)