Begin by ensuring both your source and destination Redshift clusters are set up and accessible. Make sure you have the necessary permissions to access both clusters, and confirm that they are up and running.

Modify the security group settings to allow communication between the source and destination clusters. This involves adding inbound and outbound rules that permit traffic on the necessary ports for the clusters' VPCs.

Take a snapshot of the source Redshift cluster to capture the current state of your data. This snapshot will serve as a backup and can be used to restore data if needed.

Use the UNLOAD command to export data from the source cluster to an Amazon S3 bucket. Ensure that your Redshift cluster has the necessary IAM roles and permissions to write to the S3 bucket. Example syntax:
```sql
UNLOAD ('SELECT FROM your_table')
TO 's3://your-bucket/your-path/'
CREDENTIALS 'aws_access_key_id=YOUR_ACCESS_KEY;aws_secret_access_key=YOUR_SECRET_KEY'
DELIMITER ',';
```

Ensure the destination Redshift cluster has permission to access the S3 bucket containing the unloaded data. You may need to update the bucket policy or use an IAM role that includes S3 access permissions.

Use the COPY command to load data from the S3 bucket into the destination Redshift cluster. Make sure to configure the necessary IAM permissions and specify the correct data format. Example syntax:
```sql
COPY your_table
FROM 's3://your-bucket/your-path/'
CREDENTIALS 'aws_access_key_id=YOUR_ACCESS_KEY;aws_secret_access_key=YOUR_SECRET_KEY'
DELIMITER ',';
```

After the data has been successfully loaded into the destination cluster, conduct integrity checks to ensure that the data has been transferred accurately. This could involve running checksums or comparing row counts. Once verification is complete, clean up any temporary resources like the S3 bucket contents or snapshots if no longer needed.

By following these steps, you can efficiently move data between two Redshift clusters without relying on third-party tools.