Cryptic crossword clue
Apprentice not finished, very put off suffering experience added to calendar

The most common and most likely answer to this crossword clue is the 11 letter word INTERCALARY

I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "added to calendar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case added to calendar = intercalary.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does INTERCALARY mean?

INTERCALARY adjective
  1. Describing a time period inserted between others; leap, (as in leap day, leap month, or leap year)
  2. (by extension) Inserted between other things

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