Celebrity children, not one of them accepting the present (6)
I believe the answer is:
renown
'celebrity' is the definition.
(synonyms)
'them accepting the present' is the wordplay.
'them' becomes 'ren' (I can't justify this - if you can you should give a lot more credence to this answer).
'accepting' is an insertion indicator.
'the present' becomes 'now' (now is a kind of present).
'ren' enclosing 'now' is 'RENOWN'.
'children not one of' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for renown that I've seen before include "High reputation, fame" , "Fame and public acclamation" , "Fame, respect" , "High repute" , "Plane's maximum width" .)