Humble churchman going round Middle East (6)
I believe the answer is:
demean
'humble' is the definition.
(demeaning is a kind of humbling)
'churchman going round middle east' is the wordplay.
'churchman' becomes 'dean' (I've seen this before).
'going round' means one lot of letters goes inside another.
'middle east' becomes 'me'.
'dean' placed around 'me' is 'DEMEAN'.
(Other definitions for demean that I've seen before include "Stoop" , "'Put down, degrade (6)'" , "Belittle; degrade" , "Reduce in worth" , "Lower in reputation, shame" .)