Nothing before dawn, say, is a burden (4)
I believe the answer is:
onus
'a burden' is the definition.
('onus' can be a synonym of 'burden')
'nothing before dawn say' is the wordplay.
'nothing' becomes 'o' (looks like zero - 0).
'before' means one lot of letters go next to another.
'dawn say' becomes 'nus' (I can't explain this - if you can you should believe this answer much more).
'o'+'nus'='ONUS'
'is' is the link.
(Other definitions for onus that I've seen before include "Responsibilty" , "Capulet opponent (R&J)" , "Burden, duty" , "'Burden, load (4)'" , "Obligation - charge" .)