Cause of stiffness in lead taps (6)

I believe the answer is:

starch

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'cause of stiffness' is the definition.
'starch' can be an answer for 'stiffness' (I've seen this before). I'm not sure about the 'cause of' bit.

'lead taps' is the wordplay.
'lead' becomes 'star' (synonyms).
'taps' becomes 'C H' (I've seen this in other clues).
'star'+'ch'='STARCH'

'in' is the link.

Can you help me to learn more?

(Other definitions for starch that I've seen before include "Formality - makes things stiff" , "ceremony" , "Carbohydrate; stiffener" , "Stuff that stiffens, say collars" , "Setter" .)

I've seen this clue in The Telegraph.

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