The most common and most likely answer to this crossword clue is the 7 letter word SIDLING
S
I
D
L
I
N
G
More clues leading to the result SIDLING
Buddy explains!

The straight part
We know that "Slinking away" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case slinking away = sidling.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 SIDLING mean?
SIDLING adjective- Directed toward one side
- Inclined; having an inclination
- In a sidelong direction
- Obliquely; askew
- To (cause something to) move sideways.
- In the intransitive sense often followed by up: to (cause something to) advance in a coy, furtive, or unobtrusive manner.
- The motion of one who sidles.