By default, after booking in a shipment from Brightpearl, Shiptheory sends back the tracking number to the Goods-Out Note related to the order that was booked in.
You have the option in Shiptheory to specify custom fields where Shiptheory can send back tracking information to. To find this setting navigate to your Brightpearl integration settings in Shiptheory and open the advanced settings section at the bottom of the page. Then scroll down until you see "Tracking Number Custom Field" and "Tracking Link Custom Field" options.
Both of these custom fields must be created as a sales custom field in Brightpearl and when creating the field it must have the Custom field type of Freeform text.
Once you have set up your custom fields in Brightpearl, copy the value of Field code paste it into the relevant custom field setting in Shiptheory. Make sure you save your settings in order for the change to take place.