The most common and most likely answer to this crossword clue is the 8 letter word TRIPLING
I've seen this crossword clue in The Guardian
T
R
I
P
L
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G
Buddy explains!

The straight part
We know that "growing a lot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case growing a lot = tripling.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.
Crossword Answer definitions
TRIPLING verb- To multiply by three
- To get a three-base hit
- To become three times as large
- To serve or operate as (something), in addition to two other functions.
- An act of multiplying by three.