Belittle this person being entertained by head of faculty? (6)
I believe the answer is:
demean
'belittle' is the definition.
(belittle can mean to demean or patronise)
'this person being entertained by head of faculty?' is the wordplay.
'this person' becomes 'me' (the person writing).
'being entertained by' means one lot of letters goes inside another (inserted letters are hosted or entertained).
'head of faculty?' becomes 'dean' (academic position).
'me' going within 'dean' is 'DEMEAN'.
(Other definitions for demean that I've seen before include "Debase" , "Cause (someone) to suffer loss of dignity" , "Humble" , "Degrade, humiliate" , "Lower in dignity or respect" .)