Mean with mum and the new baby (6)
I believe the answer is:
shabby
'mean' is the definition.
(thesaurus)
'mum and the new baby' is the wordplay.
'mum' becomes 'sh' (I've seen this in other clues).
'and' means one lot of letters go next to another.
'the new' indicates anagramming the letters.
'baby' is an anagram of 'abby'.
'sh'+'abby'='SHABBY'
'with' acts as a link.
(Other definitions for shabby that I've seen before include "Down at heel" , "Unworthy" , "Grotty" , "'Scruffy, tattered (6)'" , "Worn and dirty; mean" .)