Published erudition with the rude bit cut out (7)
I believe the answer is:
edition
'published erudition' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'rude bit cut out' is the wordplay.
I cannot quite see how this works, but
'bit' could be 'o' (resembles 0, a binary digit or bit) and 'o' is present in the answer.
'cut' could be 'edit' (synonyms) and 'edit' is present in the answer.
The remaining letters 'in' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'with the' acts as a link.
Can you help me to learn more?
(Other definitions for edition that I've seen before include "single programme" , "Issue; version" , "Number of copies printed at one time" , "Something impressed" , "Issue of a book" .)