Divine visitor almost succeeded (5)
I believe the answer is:
guess
'divine' is the definition.
(I've seen this before)
'visitor almost succeeded' is the wordplay.
'visitor' becomes 'guest' (guest is a kind of visitor).
'almost' means to remove the last letter (most of the word but not all of it).
'succeeded' becomes 's' (genealogical abbreviation).
'guest' with its last letter taken away is 'gues'.
'gues'+'s'='GUESS'
(Other definitions for guess that I've seen before include "shot?" , "Fancy" , "Imagine" , "Surmise" , "Make stab at" .)