Lucky dip bishop organised, backing nevertheless also required (4,3)
I believe the answer is:
Here is my best explanation:
'lucky dip' is the definition.
(I've seen this before)
I don't understand the rest of the clue.
(Other definitions for bran tub that I've seen before include "A lucky dip", "Gifts from here", "Lucky-dip container", ""Lucky dip" here", "place for a dip" and "Container for lucky dip".)