Republican bishop welcomed by curious Aegean order once more (9)
I believe the answer is:
rearrange
'order once more' is the definition.
('arrange' can be a synonym for 'order' so perhaps 'rearrange' is OK for 'order once more')
'republican bishop welcomed by curious aegean' is the wordplay.
'republican' becomes 'R' (abbreviation).
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'welcomed by' means one lot of letters goes inside another (letters welcomed inside).
'curious' indicates anagramming the letters.
'aegean' with letters rearranged gives 'eaange'.
'rr' placed inside 'eaange' is 'earrange'.
'r'+'earrange'='REARRANGE'
(Other definitions for rearrange that I've seen before include "Change the position of" , "Move round" , "Give another order" , "Tidy up" , "Order differently" .)