Psychoanalyst's right to probe rivalry (5)
I believe the answer is:
freud
'psychoanalyst's' is the definition.
(Sigmund Freud, father of psychoanalysis)
'right to probe rivalry' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to probe' indicates putting letters inside (probe can mean to poke into).
'rivalry' becomes 'feud' (I can't justify this - if you can you should give a lot more credence to this answer).
'r' inserted within 'feud' is 'FREUD'.
Can you help me to learn more?
(Other definitions for freud that I've seen before include "One introducing ID" , "See 9" , "Sigmund -, Austrian neurologist" , "Painter" , "Sigmund --, psychoanalyst" .)