Put one slice of garlic in the oil when you first turn on the heat. When it sizzles, your oil is ready for the rest of the garlic.
Whisk together lime juice and zest in a large heatproof bowl. In a small skillet, heat 5 tablespoons oil over medium-high. Add garlic and cook, stirring often, until light golden, 30 seconds to 1 minute. Whiskoil mixture into lime mixture; season with salt and pepper. Set aside 2 tablespoons dressing; add corn and tomatoes to remaining dressing and toss gently to combine. Season with salt and pepper.
Return skillet to medium-high heat and swirl in remaining 1 tablespoon oil. Add halloumi (be careful; it may splatter) and cook, flipping once, until golden and crisp on both sides, about 4 minutes total. Transfer to paper towels to drain.
Scatter arugula on a serving plate; top with corn-tomato mixture. Serve, with halloumi and reserved dressing on the side.