Rebellion finished in 2nd place in the World Endurance LMP1 Championship with 134 points, making the R13 the best of the non-hybrid cars.

On September 10, 2020, French-language magazine Auto Hebdo reported that the Signatech Alpine team competing in LMP2 during the 2019–20 WEC season would step up to the new Le Mans Hypercar class for 2021 with a re-badged R13, with agreement that LMH rules in the initial season would include an allowance to re-homologate ("grandfather") non-hybrid LMP1 cars.

[13] For LMH, the BoP fuelling limit for the A480 was set to allow 12 laps but it was not possible to physically fit this allowance into the smaller tank, and Oreca were not able to find a workaround compatible with homologation in time for the inaugural race at Spa, where the disadvantage was enough to add an extra fuel stop compared to Toyota.

During the 2021 season Alpine managed to score podiums in all six races, while also taking pole position and fastest lap at the 8 Hours of Portimão, scoring 128 points and finishing second in the Hypercar World Endurance Championship, never overcoming the stint-length deficit caused by their smaller fuel tank.

Lapierre, Negrão and Vaxivière finished 3rd as a crew in the Hypercar World Endurance Drivers' Championship with the same points tally.

On 16 February 2022 Alpine announced that the car would complete for a further and final season with the same driver line-up of Lapierre, Negrão and Vaxivière.