The most common and most likely answer to this crossword clue is the 6 letter word NAGGED
I've seen this crossword clue in Independent
N
A
G
G
E
D
More clues leading to the result NAGGED
Buddy explains!

The straight part
We know that "Went on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went on = nagged.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 NAGGED mean?
NAGGED verb- To continuously remind or complain to (someone) in an annoying way, often about insignificant or unnecessary matters.
- To bother with persistent thoughts or memories.
- To bother or disturb persistently in any way.