Mater almost sped off in panic (8)
I believe the answer is:
stampede
'panic' is the definition.
('stampede' can be a synonym of 'panic')
'mater almost sped off' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'off' is an anagram indicator.
'mater' with its last letter taken away is 'mate'.
'mate'+'sped'='matesped'
'matesped' with letters rearranged gives 'STAMPEDE'.
'in' acts as a link.
(Other definitions for stampede that I've seen before include "rush for safety maybe" , "Flight of cattle in panic" , "Headlong rush of animals" , "Sudden dash of a group of startled animals" , "Crazy pets made a sudden rush" .)