Dashes off at a crazy rate and is clearly unhappy (5,1,4)

I believe the answer is:

sheds a tear

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'is clearly unhappy' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'dashes off at a crazy rate' is the wordplay.
'off' indicates an anagram.
'at' says to put letters next to each other.
'a crazy' is an anagram indicator.
'dashes' with letters rearranged gives 'shedsa'.
'rate' with letters rearranged gives 'tear'.
'shedsa'+'tear'='SHEDS A TEAR'

'and' acts as a link.

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I've seen this clue in the Evening Standard.

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