Use it to express neutrality or a lack of support without showing active opposition. I hold no brief for either political party; my concerns are more local.
Pro Tip 2/3
Not a Defender
Suggests you're not responsible for defending someone, often due to disagreements or indifference. I hold no brief for their actions; I was not involved.
Pro Tip 3/3
Impartial View
Emphasizes an objective or impartial viewpoint, without taking sides. On the issue of funding, I hold no brief for any department.