Annoy heads of research and nearly kindle limitless enmity (6)
I believe the answer is:
rankle
'annoy' is the definition.
(I know that rankle is a more specific form of annoy)
'heads of research and nearly kindle limitless enmity' is the wordplay.
'heads of' suggests taking the first letters.
The initial letters of 'research and nearly kindle limitless enmity' is 'RANKLE'.
(Other definitions for rankle that I've seen before include "Cause long-term irritation" , "Eat into and cause resentment" , "Gnaw away at" , "Cause continuous irritation" , "Stick in one's craw" .)