The most common and most likely answer to this crossword clue is the 6 letter word GELATO
I've seen this crossword clue in The Sunday Telegraph
G
E
L
A
T
O
More clues leading to the result GELATO
- Try to keep story up - it's ice-cream!
- Posh girl half atones, making ice-cream
- Legend in game, but not going down a treat in Milan?
- Set upon endless path with love — sweet!
- Try including story about ice cream
- Try covering story about part of fare to Italy?
- Come together at Oval for dessert
- Try to catch lift that’s not closed — it will disappear at a lick!
- A stocking-filler turning to ice
- Story read backwards during journey, sweet
Buddy explains!

The straight part
We know that "sweet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sweet = gelato.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 GELATO mean?
GELATO noun- An Italian variant of ice cream made from milk and sugar, combined with other flavourings. The ingredients are supercooled while stirring to break up ice crystals as they form.