Munster began rallying as a co-driver for his father Bernard, debuting at the Terre de Lozère Rally in 2015. In 2016, the Munster pairing won the Rally Nationale Terre de Vaucluse, with Grégoire co-driving a Porsche 911 Carrera RS Proto. He transitioned to driving in 2017, finishing sixth in the ADAC Opel Rallye Cup. In 2018, he won three rounds of the Opel Cup, finished second in the overall standings, and claimed the Belgian Junior Rally Championship with four victories in an Opel Adam R2.
Munster made his European Rally Championship debut in 2018 and stepped up to the ERC3 Junior category the following year with the ADAC Opel Rallye Junior Team, recording a best result of fourth in Spain. He also retained the Belgian Junior title in 2019, winning four of the first five rounds, and made his WRC debut at the Monte Carlo Rally in a Škoda Fabia R5.
For 2020, Munster joined Hyundai's junior programme, competing in the ERC full-time in the Hyundai i20 R5 alongside co-driver Louis Louka. He claimed his first ERC podium and first ERC stage win in Portugal, added second at Hungary, but lost the ERC1 Junior title after a puncture at the Rally Islas Canarias, finishing third in the standings. He also made several WRC starts in WRC2 machinery during the year.
In 2021, Munster focused on the Belgian Rally Championship with Hyundai, taking two victories to finish second overall alongside Louka. He also competed in two WRC3 events, winning seven stages including the Power Stage at the Ypres Rally.
Munster joined Hyundai's Customer Racing Junior Driver programme in 2022, contesting selected WRC2 rounds. He scored a maiden WRC2 class victory in Japan and finished ninth in the WRC2 championship. Fans voted him the most improved WRC driver of 2022.
For 2023, Munster left Hyundai and signed with M-Sport Ford, continuing in WRC2 while beginning a relationship with the British team. During the season, he made his Rally1 top-class debut at the Rally Chile in a car entered by team partner Jourdan Serderidis, performing securely in mixed conditions. He followed that with a strong run at the Central European Rally before retiring late from WRC2 contention in Japan.
With Ott Tänak's departure from M-Sport, Munster was promoted to a full-time Rally1 seat for the 2024 WRC season, described by the team as a learning year. Short on mileage relative to more experienced rivals, he struggled with errors in several events including Monte Carlo and Finland, but improved in the second half of the year to claim two successive fifth-place finishes at the Central European Rally and in Japan.
Retained by M-Sport for 2025 and elevated to team leader status following Adrien Fourmaux's departure, Munster showed improved pace throughout the season. He claimed a maiden Rally1 stage win in Monte Carlo stage 10, took fifth in Kenya while managing suspension damage and a family bereavement, and ran sixth in Greece before mechanical failure ended his run. He finished tenth in the 2025 WRC championship, the highest of the M-Sport Ford drivers.
Munster was replaced by Jon Armstrong on M-Sport's 2026 lineup but was given the opportunity to conclude his Rally1 tenure with a start at the 2026 Monte Carlo Rally before departing the team.
Munster's career reflects the path of a second-generation rally driver who earned his factory opportunities through consistent junior-series results rather than inherited advantage. His WRC2 victory in Japan in 2022, his promotion to M-Sport's full-time seat, and his status as the top-ranked M-Sport driver across 2025 mark him as one of the notable emerging talents from the Benelux region in international rallying.