Mark East gives us a fright (5)

I believe the answer is:

scare

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'a fright' is the definition.
(scare is a kind of fright)

'mark east' is the wordplay.
'mark' becomes 'scar' ('scar' can be a synonym of 'mark').
'east' becomes 'e' ('E' can be a synonym of 'east').
'scar'+'e'='SCARE'

'gives us' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for scare that I've seen before include "Startle" , "Health worry" , "Frighten or intimidate" , "Frighten, alarm" , "Greatly frighten" .)

I've seen this clue in the Evening Standard.

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