Certainly! Assuming you have an "orders" table, you can use the following SQL query to add a "status" column with a default value of 'PENDING' and set it to 'COMPLETE' if the "completed_at" column is not null:
```sql
ALTER TABLE orders
ADD COLUMN status VARCHAR(10) DEFAULT 'PENDING' NOT NULL;
UPDATE orders
SET status = 'COMPLETE'
WHERE completed_at IS NOT NULL;
```
This query first adds the "status" column to the "orders" table with a default value of 'PENDING'. Then, it updates the "status" to 'COMPLETE' for rows where the "completed_at" column is not null. Adjust the data types and column names as needed based on your specific table structure.