Cook fennel, celery, and garlic: Heat oil in a large straight-sided skillet over medium-high heat. Add fennel, celery, and garlic and cook, stirring frequently, until tender and deep golden, about 8 minutes. Remove from heat.
Cook pasta; reserve water and drain: Meanwhile, bring a pot of generously salted water to a boil. Cook pasta according to package instructions. Reserve 1 cup pasta water; drain.
Combine pasta and pasta water with vegetables: Add pasta and pasta water to skillet with vegetables. Cook over medium-high heat, stirring to coat pasta, until warmed through, 2 to 3 minutes.
Add fennel fronds, celery leaves, and zest: Stir in fennel fronds, celery leaves, and lemon zest.
Fold in sardines; season and drizzle with oil: Break up sardines into large pieces and gently fold into pasta. Season with salt and pepper and drizzle with oil.
