The most common and most likely answer to this crossword clue is the 6 letter word TIPTOE
I've seen this crossword clue in The Sunday Telegraph
T
I
P
T
O
E
More clues leading to the result TIPTOE
- Advice to leader of expedition — proceed with caution
- Move carefully, spinning top in game
- Hint to leader of expedition to move stealthily
- Turn over new leaf in bond? Tread softly
- Hint to English – tread carefully!
- It upset poet terribly to move with discretion
- Advice given to middlemen — move quietly
- Hint at member to go quietly
- This pot some occasionally steal
- Steal look over widening moor
Buddy explains!

The straight part
We know that "Walk quietly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case walk quietly = tiptoe.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 TIPTOE mean?
TIPTOE noun- (usually in the plural) The tip of the toe.
- To walk quietly with only the tips of the toes touching the ground.
- Standing elevated, on or as if on the tips of one's toes.
- Moving carefully, quietly, warily or stealthily, on or as if on the tips of one's toes.