Sure, here's a SQL query to achieve that:
```sql
ALTER TABLE orders
ADD COLUMN status VARCHAR(20) DEFAULT 'PENDING';
UPDATE orders
SET status = 'COMPLETE'
WHERE completed_at IS NOT NULL;
```
This query first alters the table `orders` to add a new column called `status` with a default value of 'PENDING'. Then, it updates the `status` column to 'COMPLETE' for rows where the `completed_at` column is not null, indicating that the order has been completed.
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