Non-clergy's short joke about wedding (7)

I believe the answer is:

nuptial

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'wedding' is the definition.
(I've seen this before)

'non-clergy's short joke about' is the wordplay.
'non clergy's short' becomes 'lait' (I am not sure about this - if you are sure you should believe this answer much more).
'joke' becomes 'pun' (pun is a type of joke).
'about' is a reversal indicator.
'lait'+'pun'='laitpun'
'laitpun' reversed gives 'NUPTIAL'.

Can you help me to learn more?

(Other definitions for nuptial that I've seen before include "Pertaining to weddings" , "To do with marriage or a wedding ceremony" , "Relating to matrimony" , "Relating to weddings" , "Relating to marriage" .)

I've seen this clue in The Times.

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