Crossword Genius

Parson popular with Latin faculty? (9)

Ross

I believe the answer is:

incumbent

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'parson' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'popular with latin faculty?' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'with' says to put letters next to each other.
'latin faculty?' becomes 'cumbent' (I can't justify this - if you can you should believe this answer much more).
'in'+'cumbent'='INCUMBENT'

Can you help me to learn more?

(Other definitions for incumbent that I've seen before include "Mandatory" , "official?" , "Person in office" , "What's obligatory" , "vicar?" .)

I've seen this clue in The Times.
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