It lends inflexibility to a leader at church (6)

I believe the answer is:

starch

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'it lends inflexibility' is the definition.
The definition suggests a singular noun which matches the answer.

'leader at church' is the wordplay.
'leader at' becomes 'star' (I am not sure about this - if you are sure you should believe this answer much more).
'church' becomes 'ch' (abbreviation on maps etc).
'star'+'ch'='STARCH'

'to a' is the link.

Can you help me to learn more?

(Other definitions for starch that I've seen before include "foodstuff" , "Stiffness of manner" , "Stiffening agent" , "Carbohydrate; stiffen" , "Formal quality" .)

I've seen this clue in the Evening Standard.

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