ShareGate Desktop carries your associated permissions during a migration, and will attempt to preserve their integrity from the source to the destination whenever possible.
This article explains what happens to your permissions when running a Copy Content migration.
Users and groups Association (automatic mapping)
Your users and groups are automatically mapped at the destination. This association is done through the SharePoint people picker to preserve your permissions, and Person or Group metadata values.
Permissions on Documents, Folders, and List Items
By default, we try to preserve the permissions as they are on your items.
If some items have inherited permissions at the source, we will let them inherit the permissions from the list or library at the destination.
To preserve the list or library permissions from the source, you must copy the entire list or library using Copy Structure.
You can chose not to keep the custom permission on your items using the Configuration menu in Copy Options. This will simply restore inheritance on all the items at the destination.
Note: Custom permissions are only copied for the items they are associated with. If you uncheck preserve custom permissions in your Copy Options, you will have to re-copy the items with the associated permissions again should you decide you want the permissions (you cannot copy permissions separately at a later time). Incremental copy will not bring over new permissions from the source since the permission change doesn't leave a timestamp (modified) on the item in SharePoint.