TARGET_TAG="hoge"
aws ec2 describe-instances \
    --filter "Name=instance-state-name,Values=running" "Name=tag:Name,Values=${TARGET_TAG}" \
    | jq -r '.Reservations[].Instances[] | .PrivateIpAddress '

ec2:DescribeInstancesポリシーが必要。

環境

$ aws --version
aws-cli/2.17.41 Python/3.11.9 Linux/6.1.102-111.182.amzn2023.x86_64 exec-env/CloudShell exe/x86_64.amzn.2023