Desire what church will often support (6)

I believe the answer is:

aspire

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'desire' is the definition.
(thesaurus)

I cannot understand how the rest of the clue works.

(Other definitions for aspire that I've seen before include "Hanker" , "Hope, dream" , "Have hopes (to achieve something)" , "Hope (to achieve)" , "Wish to rise (to)" .)

I've seen this clue in The Times.

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