Onset of primitive impulse to eradicate (5)
I believe the answer is:
purge
'eradicate' is the definition.
(I've seen this before)
'onset of primitive impulse' is the wordplay.
'onset of' suggests taking the first letters.
'impulse' becomes 'urge' (synonyms).
The first letter of 'primitive' is 'p'.
'p'+'urge'='PURGE'
'to' acts as a link.
(Other definitions for purge that I've seen before include "Get rid of unwanted elements" , "Thoroughly clean" , "empty bowels" , "Remove undesirable elements" , "Remove by cleansing" .)