The most common and most likely answer to this crossword clue is the 14 letter word STEPPING-STONE
I've seen this crossword clue in Independent
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More clues leading to the result STEPPING-STONE
Buddy explains!

The straight part
We know that "means to get better" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case means to get better = stepping-stone.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 STEPPING-STONE mean?
STEPPING-STONE noun- A stone that can be stepped on in crossing something, especially a marsh or creek.
- Something used as a way to progress to something or somewhere else.