The most common and most likely answer to this crossword clue is the 6 letter word SKATER
I've seen this crossword clue in The Guardian
S
K
A
T
E
R
More clues leading to the result SKATER
- Heartless sir grabbing woman — one may be on thin ice!
- Run after small girl, who may be on thin ice
- ‘Little sister,’ princess admitted, ‘is smooth mover‘
- Fish by river, finding one gliding on surface
- Partially risk a terrible injury on the ice.
- Society girl runs to become a sportswoman
- Cousins say fish recipe is needed
- Finally, loveless princess put on right slipper?
- Curry was a good one – odd bits of tikka cooked in spice, extremely rich, served for starters
- Participating in task, a terrific sportsperson
Buddy explains!

The straight part
We know that "who may be on thin ice" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case who may be on thin ice = skater.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 SKATER mean?
SKATER noun- A person who skates.
- A member of skateboarding subculture, characterized by dingy and baggy clothes, and often wallet chains.
- A player who is not a goaltender.
- Any of numerous hemipterous insects in the family Gerridae, which run rapidly over the surface of the water, as if skating.