Accepted with thanks by Mr Livingstone (5)
I believe the answer is:
taken
'accepted' is the definition.
('take' can be a synonym of 'accept')
'thanks by mr livingstone' is the wordplay.
I cannot quite see how this works, but
'thanks' could be 'ta' (UK informal version of 'thank you') and 'ta' is present in the answer.
'mr' could be 'ken' and 'ken' is present in the answer.
No letters remain.
This explanation may well be incorrect...
'with' acts as a link.
Can you help me to learn more?
(Other definitions for taken that I've seen before include "Transported" , "Removed, accepted" , "This is spoken for" , "Kidnapped" , "Removed; occupied" .)