The most common and most likely answer to this crossword clue is the 5 letter word WAVER
I've seen this crossword clue in The Daily Telegraph
W
A
V
E
R
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 = waver.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 WAVER mean?
WAVER noun- An act of wavering, vacillating, etc.
- Someone who waves, enjoys waving, etc.
- Someone who specializes in waving (hair treatment).
- A tool that accomplishes hair waving.
- A sapling left standing in a fallen wood.
- To sway back and forth; to totter or reel.
- To flicker, glimmer, quiver, as a weak light.
- To fluctuate or vary, as commodity prices or a poorly sustained musical pitch.
- To shake or tremble, as the hands or voice.
- To falter; become unsteady; begin to fail or give way.
- To be indecisive between choices; to feel or show doubt or indecision; to vacillate.