Mother splitting hairs and greeting sage (9)
I believe the answer is:
maharishi
'sage' is the definition.
(I've seen this before)
'mother splitting hairs and greeting' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'splitting' indicates anagramming the letters (I've seen 'split' mean this (letters split up and reassembled)).
'and' says to put letters next to each other.
'greeting' becomes 'hi' (hi is a kind of greeting).
'hairs' is an anagram of 'haris'.
'ma'+'haris'+'hi'='MAHARISHI'
(Other definitions for maharishi that I've seen before include "Hindu spiritual leader" , "Seasoned beef-pork sausage" , "Religious leader" , "leading teacher" , "Hindu instructor" .)