Many a girl shows spite (6)

I believe the answer is:

malice

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'spite' is the definition.
(synonyms)

'many a girl' is the wordplay.
'many' becomes 'M' (Roman numeral for a thousand).
'girl' becomes 'lice' (I can't justify this - if you can you should believe this answer much more).
'm'+'a'+'lice'='MALICE'

'shows' acts as a link.

Can you help me to learn more?

(Other definitions for malice that I've seen before include "Hatred" , "evil intent" , "Spite and rancour" , "'Ill-will, spite (6)'" , "Spiteful, animosity, sometimes a forethought" .)

I've seen this clue in the Evening Standard.

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