Latin American dismissing that man's fear (5)
I believe the answer is:
panic
'fear' is the definition.
(I know that panic is a type of fear)
'latin american dismissing that man's' is the wordplay.
'latin american' becomes 'hispanic' (I've seen this in another clue).
'dismissing' is a deletion indicator.
'that man's' becomes 'his' (belonging to a man).
'hispanic' with 'his' taken away is 'PANIC'.
(Other definitions for panic that I've seen before include "Blind fear" , "Sudden overpowering fear" , "State of overwhelming fear" , "Flap" , "Alarm, scare" .)