The writer left at one after church, with a hot pepper (5)
I believe the answer is:
chili
'a hot pepper' is the definition.
(I've seen this in another clue)
'the writer left at one after church' is the wordplay.
'the writer' becomes 'I' (the person who is writing these clues).
'left' says the letters should be written in reverse.
'at' becomes 'il' (I can't justify this - if you can you should give a lot more credence to this answer).
'one after' says to put letters next to each other.
'church' becomes 'ch' (abbreviation on maps etc).
'il' back-to-front is 'li'.
'i'+'li'='ili'
'ili' put after 'ch' is 'CHILI'.
'with' is the link.
Can you help me to learn more?
(Other definitions for chili that I've seen before include "African wind" , "Hot pod (US spelling)" , "Hot pepper (US spelling)" , "Spicy pepper" .)