You will need to get (or write) an app that provides a post-function that can set custom field values.
There are many on the marketplace, but I can't point at any single one because I don't know if you have other things you might want to do with it.
Atlassian's marketplace partners have had a very productive start to 2021! Since our last roundup, our developer community has added over 160 new cloud apps to the Atlassian Marketplace to help you...
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