Insinuates you can't believe what troublemaker says (7)
I believe the answer is:
implies
'insinuates' is the definition.
(I've seen this before)
'troublemaker says' is the wordplay.
'troublemaker' becomes 'imp' (little devil).
'says' becomes 'lies' (I can't explain this - if you can you should give a lot more credence to this answer).
'imp'+'lies'='IMPLIES'
'you can't believe what' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for implies that I've seen before include "Suggests or hints at meaning" , "States indirectly" , "Insinuates" .)