The most common and most likely answer to this crossword clue is the 7 letter word HEALING
I've seen this crossword clue in The Daily Telegraph
H
E
A
L
I
N
G
More clues leading to the result HEALING
Buddy explains!

The straight part
We know that "Getting better" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case getting better = healing.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 HEALING mean?
HEALING noun- The process where the cells in the body regenerate and repair themselves.
- An act of healing, as by a faith healer.
- The psychological process of dealing with a problem or problems.
- To make better from a disease, wound, etc.; to revive or cure.
- To become better or healthy again.
- To reconcile, as a breach or difference; to make whole; to free from guilt.
- To hide, conceal, and keep secret, especially for a secret society (such as the masons).
- (now especially in the phrase "hele in") To cover or conceal (a seedling, plant, roots, etc).