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

The straight part
We know that "show liveliness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case show liveliness = effervesce.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 EFFERVESCE mean?
EFFERVESCE verb- (of a liquid) to emit small bubbles of dissolved gas; to froth or fizz
- (of a gas) to escape from solution in a liquid in the form of bubbles
- (of a person) to show high spirits