In a small saucepan, combine the vinegar, pomegranate juice, and sugar. Bring to a boil over medium-high heat and whisk to dissolve the sugar. Set aside to cool.

In a blender, combine the cooled pomegranate syrup, lemon juice, and mustard. Process on medium-high speed until smooth and well combined, 15 to 20 seconds. Stop the blender and scrape down the sides of the jar with a spatula as needed.

With the blender running on low speed, slowly drizzle in the olive oil until the dressing is emulsified and thickened, about 30 seconds. Add the salt and pepper, adjusting the seasoning to taste. Transfer the dressing to an airtight container and refrigerate until ready to use.

This dressing will keep, refrigerated, for up to 7 days.