The most common and most likely answer to this crossword clue is the 8 letter word CHECKOUT
I've seen this crossword clue in The Times
C
H
E
C
K
O
U
T
Buddy explains!
The straight part
We know that "Leave to investigate the point of paying" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leave to investigate the point of paying = checkout.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 CHECKOUT mean?
CHECKOUT noun- The process of checking out of a hotel, or the latest time to vacate a room in one.
- The process of checking out items at a supermarket or library.
- The place in a supermarket where this is done.
- A test to see if some device is functioning properly.
- An inspection or investigation.