Graze the back of the neck right away (5)
I believe the answer is:
scuff
'graze' is the definition.
(thesaurus)
'back of the neck right away' is the wordplay.
'back of the neck' becomes 'scruff' (I've seen this before).
'right' becomes 'r' (common abbreviation).
'away' indicates named letters should be taken away.
'scruff' with 'r' taken out is 'SCUFF'.
'the' acts as a link.
(Other definitions for scuff that I've seen before include "drag, while walking" , "Scrape (shoes) when walking" , "Scrape (eg, a shoe)" , "Scrape (shoe, etc)" , "Scrape (shoe leather)" .)