Hi,
It depends on how you perform migration and what you migrate.
If you migrate an instance using XML backup your customfield Ids are retained. In fact, since you clone the instance you'll keep everything as they are.
If you perform a project migration using XML backup and Jira project import, per process you have to create all of the issue related entities (custom fields, workflows, priorities etc) manually, you'll have new Ids.
If you do migration by csv, json or similar, you sa as project import case.
If you use a third party app, like configuration manager, it depends on the app's implementation but I would say you'll have new customfield IDs.
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