Tick and nits bothered a nutcase (7)

I believe the answer is:

instant

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'tick' is the definition.
(both can mean a short amount of time)

'nits bothered a nutcase' is the wordplay.
'bothered' indicates anagramming the letters.
'a nutcase' becomes 'ant' (I can't explain this - if you can you should believe this answer much more).
'nits' anagrammed gives 'inst'.
'inst'+'ant'='INSTANT'

'and' is the link.

Can you help me to learn more?

(Other definitions for instant that I've seen before include "This coffee is made from powder" , "Fast, flash" , "Brief moment" , "like some coffee?" , "No need to cook" .)

I've seen this clue in the Sydney Morning Herald.

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