Bring up right to try without leader (4)
I believe the answer is:
rear
'bring up' is the definition.
(rearing is a kind of bringing up)
'right to try without leader' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to try' becomes 'hear' (as in to try someone in court or hear their case).
'without leader' means to remove the first letter.
'hear' with its initial letter removed is 'ear'.
'r'+'ear'='REAR'
(Other definitions for rear that I've seen before include "early, long before now" , "Of horse, rise up on hind legs" , "Bring up (children)" , "Rump" , "Bring up - back end" .)