The most common and most likely answer to this crossword clue is the 6 letter word TEETER
I've seen this crossword clue in The Daily Telegraph
T
E
E
T
E
R
More clues leading to the result TEETER
- Nameless youth, tense with sign of hesitation, gets to wobble
- Waver about forwarded message, ignore wife heading north
- Online poster wife leaves in lurch
- Abstainer renounces love beside lofty seesaw
- Rock & Roll Support with Queen touring Thailand
- Hesitate in start of course before short academic period
- Where driver begins, note, on surface of road to hesitate?
- . Rock forcing son to make way for the bridge player with a canopy
- Support beneath terrace shifts position to sway unsteadily
- The essence of sedate eternity is balance
Buddy explains!

The straight part
We know that "Hesitate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hesitate = teeter.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 TEETER mean?
TEETER noun- A teeter-totter or seesaw.
- To tilt back and forth on an edge.
- To be indecisive.
- To be close to becoming a typically negative situation.