The most common and most likely answer to this crossword clue is the 5 letter word LEGIT
I've seen this crossword clue in Financial Times
L
E
G
I
T
Buddy explains!

The straight part
We know that "Authorised/to go away on foot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case authorised/to go away on foot = legit.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 LEGIT mean?
LEGIT noun- A legitimate; a legitimate actor.
- A legitimate child.
- Legitimate; legal; allowed by the rules; valid.
- (by extension, of a thing or person) Genuine, actual, literal or honest.
- Genuinely good and possessing all the required or expected qualities; the real deal.
- Cool by virtue of being genuine.
- Legitimately; within the law.
- Honestly; truly; seriously.