Bring up the back (4)
I believe the answer is:
Here is my best explanation:
This clue is a double definition.
'bring up' is the first definition.
(rearing is a kind of bringing up)
'the back' is the second definition.
('rear' can be a synonym of 'back')
(Other definitions for rear that I've seen before include "Foster", "Raise; behind", "Bring up - the tail", "It's rare at the back", "Bring up (or what you can bring up!)", "Hindmost part", "Bring up or stand up on hind legs", "Posterior", "Bring up (children)" and "Stern".)