The most common and most likely answer to this crossword clue is the 8 letter word OUTGROWN
I've seen this crossword clue in Financial Times
O
U
T
G
R
O
W
N
Buddy explains!
The straight part
We know that "Got too big" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case got too big = outgrown.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 OUTGROWN mean?
OUTGROWN verb- To become too big in size or too mature in age or outlook to continue to want, need, use, experience, or accept some object, practice, condition, belief, etc.
- To grow faster or larger than.