Belittle egghead in named organisation (6)
I believe the answer is:
demean
'belittle' is the definition.
(belittle can mean to demean or patronise)
'egghead in named organisation' is the wordplay.
'egghead' becomes 'e' (head letter of 'egg').
'in' is an insertion indicator.
'organisation' indicates anagramming the letters.
'named' anagrammed gives 'deman'.
'e' placed inside 'deman' is 'DEMEAN'.
(Other definitions for demean that I've seen before include "Belittle; degrade" , "Lower in reputation, shame" , "Stoop" , "disgrace" , "'Put down, degrade (6)'" .)