The most common and most likely answer to this crossword clue is the 10 letter word POPULARITY
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More clues leading to the result POPULARITY
Buddy explains!

The straight part
We know that "adulation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case adulation = popularity.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 POPULARITY mean?
POPULARITY noun- The quality or state of being popular; especially, the state of being esteemed by, or of being in favor with, the people at large
- The quality or state of being adapted or pleasing to common, poor, or vulgar people; hence, cheapness; inferiority; vulgarity.
- Something which obtains, or is intended to obtain, the favor of the vulgar; claptrap.
- The act of courting the favour of the people.
- Public sentiment; general passion.