Neurologist foregoing right to indulge in quarrel (4)
I believe the answer is:
feud
'indulge in quarrel' is the definition.
(to feud is to have a quarrel)
'neurologist foregoing right' is the wordplay.
'neurologist' becomes 'freud' (Sigmund Freud).
'foregoing' suggests deleting specific letters (to forgo something is to give it up).
'right' becomes 'r' (abbreviation).
'freud' with 'r' removed is 'FEUD'.
'to' acts as a link.
(Other definitions for feud that I've seen before include "Persistent strife" , "Prolonged dispute" , "Long-running dispute" , "Lasting hostility between people or groups" , "Prolonged quarrel" .)