The most common and most likely answer to this crossword clue is the 8 letter word DIRECTLY
I've seen this crossword clue in The Guardian
D
I
R
E
C
T
L
Y
Buddy explains!

The straight part
We know that "right away" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case right away = directly.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 DIRECTLY mean?
DIRECTLY adverb- In a direct manner; in a straight line or course.
- In a straightforward way; without anything intervening; not by secondary, but by direct means.
- Plainly, without circumlocution or ambiguity; absolutely; in express terms.
- Exactly; just.
- Straightforwardly; honestly.
- Immediately.
- Soon; next; when it becomes convenient.
- As soon as; immediately.