The most common and most likely answer to this crossword clue is the 2 plus 4 letter word LE MANS
I've seen this crossword clue in The Daily Telegraph
L
E
M
A
N
S
More clues leading to the result LE MANS
- Old-fashioned sweetheart's somewhere in France
- French race venue tends to receive millions
- Celebrity raised in outskirts of Limoges, French city
- City‘s bankrupt financiers, hard to ignore
- Scene of motor race with bends covering miles
- Lists including motorway as place to race
- Slowcoach ropes me in, for one, to move up in race situation
- Monaco’s first in lists as race venue
- Celebrity left, turning back on small French city
- Where people go round night and day getting to the heart of problem answers
Buddy explains!

The straight part
We know that "Where people go round night and day" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where people go round night and day = le mans.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.