Cryptic crossword clue
Going off over key lessees sounding difficult to please 4,11

The most common and most likely answer to this crossword clue is the 4 plus 11 letter word HIGH MAINTENANCE

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Buddy explains!

The straight part
We know that "difficult to please" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case difficult to please = high maintenance.
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 HIGH MAINTENANCE mean?

HIGH MAINTENANCE adjective
  1. Of a system: requiring a high degree of maintenance to ensure proper functioning, and without which it is likely to break down.
  2. (of a person) requiring a lot of attention or reassurance; emotionally needy

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