...bound to make legislator accept central lies (4)
I believe the answer is:
tied
'bound' is the definition.
('tie' can be a synonym of 'bind')
'legislator accept central lies' is the wordplay.
'legislator' becomes 'td' (I can't justify this - if you can you should believe this answer much more).
'accept' indicates putting letters inside.
'central' says to take the centre.
The middle of 'lies' is 'ie'.
'td' placed around 'ie' is 'TIED'.
'to make' acts as a link.
Can you help me to learn more?
(Other definitions for tied that I've seen before include "Bonded" , "Restricted, bound" , "Drawn" , "In no-win situation" , "Fastened, bound" .)