Reader worried by Burke or Hare finally choosing body (10)
I believe the answer is:
electorate
'choosing body' is the definition.
(body of people choosing or electing someone)
'reader worried by burke' is the wordplay.
'reader' becomes 'lector' (synonyms).
'worried' becomes 'ate' (something worrying may eat someone up).
'by' says to put letters next to each other.
'burke' becomes 'e' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lector'+'ate'='lectorate'
'lectorate' put after 'e' is 'ELECTORATE'.
'or hare finally' acts as a 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 electorate that I've seen before include "Those entitled to vote" , "Voters collectively" , "Those qualified to vote" , "Voters in general" , "Voters as a whole" .)