Men occupied with prediction as overheard, speaking persuasively (10)
I believe the answer is:
oratorical
'speaking persuasively' is the definition.
(oratory is persuasive public speaking)
'men occupied with prediction as overheard' is the wordplay.
I cannot really understand how this works, but
'men' could be 'or' (military abbreviation for Other Ranks) and 'or' is located in the answer.
'occupied' could be 'at' (being occupied or busy at something) and 'at' is found in the answer.
This explanation may well be incorrect...
(Another definition for oratorical that I've seen is " Relating to public speaking".)