Uber’s top executives spent Tuesday evening at a hastily arranged dinner in San Francisco, gabbing and drinking with their new CEO, Dara Khosrowshahi. Several board members, including former CEO Travis Kalanick, also attended. On Wednesday, they were all smiles again at Mr. Khosrowshahi’s first all-hands meeting with Uber employees. But those happy expressions disguised rising tensions within the management team. At issue: Human Resources chief Liane Hornsey’s overhaul of Uber’s HR practices.

And as they prepare for Mr. Khosrowshahi to take the reins next week, Ms. Hornsey and her colleagues are girding for a fight to sway him to one side or the other. At the heart of the battle is a question of how to reward the top performers. Ms. Hornsey wants to eliminate stark pay discrepancies between employees in similar roles and avoid excessive preferential treatment for the best people.

But a host of other senior executives—including data science and growth chief Daniel Graf, engineering chief Thuan Pham, security chief Joe Sullivan and AI lab chief Jeff Holden—are fighting to preserve certain practices, including the ability to pay generous bonuses to certain top performers, which the executives see as key to retaining talent.