The most common and most likely answer to this crossword clue is the 4 letter word BORE
I've seen this crossword clue in Financial Times
B
O
R
E
More clues leading to the result BORE
Buddy explains!

The straight part
We know that "I go on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i go on = bore.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 BORE mean?
BORE noun- A hole drilled or milled through something, or (by extension) its diameter.
- The tunnel inside of a gun's barrel through which the bullet travels when fired, or (by extension) its diameter.
- A tool, such as an auger, for making a hole by boring.
- A capped well drilled to tap artesian water. The place where the well exists.
- One who inspires boredom or lack of interest; an uninteresting person.
- Something dull or uninteresting
- Calibre; importance.
- To inspire boredom in somebody.
- To make a hole through something.
- To make a hole with, or as if with, a boring instrument; to cut a circular hole by the rotary motion of a tool.
- To form or enlarge (something) by means of a boring instrument or apparatus.
- To make (a passage) by laborious effort, as in boring; to force a narrow and difficult passage through.
- To be pierced or penetrated by an instrument that cuts as it turns.
- To push forward in a certain direction with laborious effort.
- (of a horse) To shoot out the nose or toss it in the air.
- To fool; to trick.
- A sudden and rapid flow of tide occuring in certain rivers and estuaries which rolls up as a wave.
- To carry or convey, literally or figuratively.
- To support, sustain, or endure.
- To support, keep up, or maintain.
- To press or impinge upon.
- To produce, yield, give birth to.
- (originally nautical) To be, or head, in a specific direction or azimuth (from somewhere).
- To gain or win.