Less well-known owner giving mild rebuke (3,3)
I believe the answer is:
now now
'mild rebuke' is the definition.
('now, now' might be said to rebuke someone)
'less well-known owner' is the wordplay.
'less' says the answer is hidden in the clue (the clue less some of the letters in it).
'NOW NOW' is hidden in the letters of 'well known owner'.
'giving' is the link.
(Other definitions for now now that I've seen before include "said to calm one down" , "Warning" , "It's said to reprimand or pacify a person" , "stop bickering" .)