To add a time entry with a one-off custom billing rate, go to any existing work item and click the 'Time & Budget' tab.
First, create a budget estimate for at least the Role / Task Type combo using your desired custom billing rate. Don't select 'Use Default'. Rather, enter your desired hourly rate.
Next, create a time entry that matches the combination of Role / Task Type combo you provided above. By doing so, Karbon will match the budget estimate to the actual time entry you have provided and associate the right billing rate to the activity completed.
Remember, Karbon will match to a budget estimate first to obtain the proper billing rate. If it can't match, then Karbon will use the default billing rate for the given role / task type combo.