This is probably doable in a flow... but the to do this in a trigger, there are some generic steps that you can follow.
Get get all the carrier product ids. Put them in a list or a set by looping
Trigger.new
Query the
Carrier_Product__c
object to get the checkbox field that you want. eg[SELECT Id, Rebalance__c FROM Carrier_Product__c WHERE Id IN :carrierProductIdList ];
Put the results of this query into a
Map<Id,Carrier_Product__c>
Loop
Trigger.new
and use the product id to get the correct carrier product out of the map.Examine the value and set/unset the checkbox.
This should be a before trigger, so you don't need to update.