The most common and most likely answer to this crossword clue is the 10 letter word RESPONSIVE
I've seen this crossword clue in The Sunday Telegraph
R
E
S
P
O
N
S
I
V
E
Buddy explains!

The straight part
We know that "quick to react" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quick to react = responsive.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 RESPONSIVE mean?
RESPONSIVE adjective- Answering, replying or responding
- Able to receive and respond to external stimuli
- Using antiphons; antiphonal
- Susceptible to the feelings of others
- Automatically resizing and repositioning elements to fit the available space
- Suited to something else; correspondent
- Responsible