The most common and most likely answer to this crossword clue is the 6 letter word PUTTER
I've seen this crossword clue in The Daily Telegraph
P
U
T
T
E
R
More clues leading to the result PUTTER
- Club page complete
- Piano, say, for club
- Speak, under pressure, in golf club
- Total behind back of strip club
- Speak, after end of championship, in golf club
- Club for Green Party leader, say
- Make publicly known at opening of parish club
- Pressure to speak in golf club
- Implement of Green power, say?
- Parking, say, in golf club
Buddy explains!

The straight part
We know that "the man playing on the green" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the man playing on the green = putter.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 PUTTER mean?
PUTTER verb- To be active, but not excessively busy, at a task or a series of tasks.
- One who puts or places.
- A shot-putter.
- One who pushes the small wagons in a coal mine.
- A golf club specifically intended for a putt.
- A person who is taking a putt or putting.
- To produce intermittent bursts of sound in the course of operating.