Burden with broken ladders, with no right! (6)
I believe the answer is:
saddle
'burden' is the definition.
('saddle' can be a synonym of 'burden')
'broken ladders with no right' is the wordplay.
'broken' indicates an anagram.
'with no' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'ladders' with 'r' taken out is 'laddes'.
'laddes' with letters rearranged gives 'SADDLE'.
'with' is the link.
(Other definitions for saddle that I've seen before include "land" , "Chafed by riding" , "Burden; seat" , "Jockey's seat" , "Impose a task on -- assign responsibility for" .)