Slice the red snapper into thin, even pieces (about ⅛-inch thick). Arrange on a chilled plate.
In a small bowl, mix harissa paste with olive oil to create a smooth drizzle. Toss the cherry tomato slices with a pinch of salt, letting them sit for a minute to release juices.
Drizzle the harissa mixture over the snapper. Scatter the salted cherry tomatoes and minced preserved lemon across the plate. Garnish with cilantro leaves. Serve immediately.