New clue's badly constructed using indicator, initially for 'middle parts' (6)
I believe the answer is:
nuclei
'parts' is the definition.
(nucleus is a kind of part)
'new clue's badly constructed using' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'badly' indicates an anagram (letters in the wrong order).
'constructed using' becomes 'i' (I can't explain this - if you can you should believe this answer much more).
'clue' with letters rearranged gives 'ucle'.
'n'+'ucle'+'i'='NUCLEI'
'indicator initially for middle' 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 nuclei that I've seen before include "Kernels" , "Atom cores" , "Central parts of atoms" , "Central pieces" , "Bases" .)