The most common and most likely answer to this crossword clue is the 11 letter word EXAMINATION
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More clues leading to the result EXAMINATION
Buddy explains!

The straight part
We know that "check-up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case check-up = examination.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 EXAMINATION mean?
EXAMINATION noun- The act of examining.
- Particularly, an inspection by a medical professional to establish the extent and nature of any sickness or injury.
- A formal test involving answering written or oral questions under a time constraint and usually without access to textbooks.
- Interrogation.