Mark East gives us a fright (5)
I believe the answer is:
scare
'a fright' is the definition.
(scare is a kind of fright)
'mark east' is the wordplay.
'mark' becomes 'scar' (mark left by an injury).
'east' becomes 'e' (abbreviation).
'scar'+'e'='SCARE'
'gives us' is the link.
(Other definitions for scare that I've seen before include "Startle" , "Health worry" , "Frighten or intimidate" , "Frighten, alarm" , "Greatly frighten" .)