Beginning to document setter's fall (4)
I believe the answer is:
dive
'fall' is the definition.
(diving is a kind of falling)
'beginning to document setter's' is the wordplay.
'beginning to' says to take the initial letters.
'setter's' becomes 'ive' ('I've', referring to the crossword setter).
The first letter of 'document' is 'd'.
'd'+'ive'='DIVE'
(Other definitions for dive that I've seen before include "Swim under water" , "Joint" , "Plunge into - disreputable club" , "Plunge into a low haunt" , "Disreputable establishment" .)