The most common and most likely answer to this crossword clue is the 8 letter word SCENTING
I've seen this crossword clue in The Daily Telegraph
S
C
E
N
T
I
N
G
More clues leading to the result SCENTING
Buddy explains!

The straight part
We know that "Becoming aware" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case becoming aware = scenting.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 SCENTING mean?
SCENTING verb- To detect the scent of; to discern by the sense of smell.
- To have a suspicion of.
- To impart an odour to.
- To have a smell.
- To hunt animals by means of the sense of smell.
- The act or process by which something is scented.