The longevity and consistency of the grip level can be increased by properly scuffing a new set of race tires. It's very important not to run hard for an entire session on new tires. Think of it like breaking in a new engine, or bedding in new brakes.
To scuff a set of tires, start by taking two or three moderately paced laps to gradually bring the tires up to operating temperature, and then run one hard lap followed by a cool down lap. The ideal situation would be to stop and remove the tires from the car, and allow them to cool down to ambient temperature before running them again.
When running an entire session on a new set of tires without stopping, one should still follow the scuffing procedure at the beginning of the session before turning laps at a fast pace. It’s also very important to run a slower lap at some point in the middle of the session to allow the tires to cool off before running hard laps again.