The most common and most likely answer to this crossword clue is the 10 letter word TREMENDOUS
I've seen this crossword clue in The Guardian
T
R
E
M
E
N
D
O
U
S
More clues leading to the result TREMENDOUS
- Great unorthodox priest's last sermon due
- Our set raving about repair that's fantastic
- Immense monster due to be beaten
- Huge demo turns nasty around the middle of Whitehall
- Huge monster due to run amok
- Super finding change in pocket when short of a sovereign
- Giant monster due to erupt
- Three regular soldiers make America great
- Great model’s about to get well, ring America!
- Some turned out great
Buddy explains!

The straight part
We know that "very big" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very big = tremendous.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 TREMENDOUS mean?
TREMENDOUS adjective- Awe-inspiring; terrific.
- Notable for its size, power, or excellence.
- Extremely large (in amount, extent, degree, etc.) or great