The most common and most likely answer to this crossword clue is the 5 letter word AWARE
I've seen this crossword clue in The Times
A
W
A
R
E
More clues leading to the result AWARE
- Knowing a king is held in great respect
- Conscious reverence when a queen enters
- Knowing a type of pottery
- Well-briefed army leader fighting English
- Knowing a sport will be broadcast
- A revolutionary green energy that's switched-on
- Conscious of feature missing in tea set
- Enlightened American overcoming battle with drug
- Informed of fighting in A&E
- Informed of fighting in A & E
Buddy explains!

The straight part
We know that "Conscious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conscious = aware.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 AWARE mean?
AWARE adjective- Vigilant or on one's guard against danger or difficulty.
- Conscious or having knowledge of something.