Left parent scratching head in a state of agitation (6)
I believe the answer is:
lather
'a state of agitation' is the definition.
(as in the phrase 'in a lather')
'left parent scratching head' is the wordplay.
'left' becomes 'l' (common abbreviation).
'parent' becomes 'father' (father is a kind of parent).
'scratching head' means to remove the first letter.
'father' with its initial letter taken off is 'ather'.
'l'+'ather'='LATHER'
'in' is the link.
(Other definitions for lather that I've seen before include "Agitated state" , "Frothy suds" , "Whip up froth - tizzy" , "Foam made from soap" , "Turner" .)