The most common and most likely answer to this crossword clue is the 6 letter word DIETED
D
I
E
T
E
D
Buddy explains!

The straight part
We know that "went on fast" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went on fast = dieted.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 DIETED mean?
DIETED verb- To regulate the food of (someone); to put on a diet.
- To modify one's food and beverage intake so as to decrease or increase body weight or influence health.
- To eat; to take one's meals.
- To cause to take food; to feed.