'local custom' is correct and usable in written English.
You can use it when talking about the traditions and practices of a specific area or locality. For example, "In this small town, it's a local custom to tip your hat when you pass someone on the street."
Exact(60)
The birds are followers of local custom.
"Eating dog meat is their local custom.
And by local custom, she is barred from remarrying.
Native chiefs were invited to hear cases involving local custom.
Anticipating the placement of the barriers at Marble Avenue has become local custom.
"The Constitution prevailed over reckless disregard for temperance, tax collection and local custom," Ms. Duggan said.
The beliefs of the militants who took control in 2012 clashed with local custom.
A policeman had to calm him down and explain it was just the local custom.
What if the suits in New York didn't understand this local custom?
It takes tact, sensitivity and astuteness to oppose an entrenched local custom.
By local custom, they should then be safe from acts of revenge.
Related(19)
local personalization
local customisation
local practice
local customization
partial custom
municipal custom
local tradition
communal custom
domestic custom
indigenous custom
local customizable
local personalized
local practices
local tailored
community custom
on site custom
local customs
local customary
local customized
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com