The most common and most likely answer to this crossword clue is the 15 letter word CONGRATULATIONS
I've seen this crossword clue in The Daily Telegraph
C
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More clues leading to the result CONGRATULATIONS
- Well done! Saluting cartoon Goofy
- Best wishes playing on an actor’s guilt
- Wind cannot tug sailor hats off
- Sort out Anglican in reformation giving praise
- Onion glut a cart’s transporting produces ‘bouquet‘
- ‘Well done’ sirloin-cut I rejected: Aga not working!
- Cliff hit Norway in a nostalgic tour that’s rocking
Buddy explains!

The straight part
We know that "Best wishes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case best wishes = congratulations.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 CONGRATULATIONS mean?
CONGRATULATIONS noun- The act of congratulating.
- Expressing praise and approval, expressing approbation.