Notorious anti-communist is in vehicle heading off to Athy, after seeing host (8)
I believe the answer is:
mccarthy
'notorious anti-communist' is the definition.
I can't judge whether this definition defines the answer.
'in vehicle heading off to athy after seeing host' is the wordplay.
'in vehicle' becomes 'car' (I can't explain this - if you can you should give a lot more credence to this answer).
'heading off' means to remove the first letter.
'after' says to put letters next to each other.
'seeing host' becomes 'mc' (short for Master of Ceremonies).
'athy' with its first letter removed is 'thy'.
'car'+'thy'='carthy'
'carthy' put after 'mc' is 'MCCARTHY'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for mccarthy that I've seen before include "anti-Communist crusader" , "US anti-communist senator of the 1950s" , "Witch-hunter" .)