The most common and most likely answer to this crossword clue is the 8 letter word OVERGREW
I've seen this crossword clue in Independent
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More clues leading to the result OVERGREW
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 = overgrew.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 OVERGREW mean?
OVERGREW verb- To grow beyond one's boundaries or containment, or beyond the proper size.
- To grow over; (of one thing) to cause (a second thing) to become overgrown (with or by the first thing).