Grist began in road rallying in Wales after taking Sundays off from a car sales job, entering his first rally — the George Ford Pips Rally in Caldicott — in a Ford Escort. Through the 1980s he built his skills in Welsh and British national championships, winning the Welsh Road Rally Championship in 1983. He made his first WRC appearance at the 1985 Lombard RAC Rally with Stuart Nicholls in a Vauxhall Astra GTE. By 1990 Grist had turned fully professional, co-driving for Ford with Malcolm Wilson in the British Open Championship and taking on WRC events.
In 1993 Grist joined the Mitsubishi works entry alongside Armin Schwarz, but partway through the season paired with Juha Kankkunen at the Rally Argentina — taking his first WRC victory. The partnership continued with Toyota and Kankkunen won that season's World Rally Championship, his fourth title, with Grist reading pace notes for the championship-deciding rounds. Toyota were subsequently banned for twelve months after the 1995 season for illegal turbo restrictor bypasses on their ST205 cars, interrupting Grist and Kankkunen's momentum.
In 1997 Grist joined the 555 Subaru World Rally Team as Colin McRae's co-driver on a two-year contract. Their first season together produced five wins and second place in the championship, with Subaru taking the manufacturers' title. In 1998 Grist took his first tarmac win alongside McRae in Corsica, and Subaru claimed their third consecutive manufacturers' championship.
The pair moved to M-Sport Ford in 1999 with the new Focus WRC, winning consecutively at the Safari Rally and Rally Portugal before reliability issues limited their championship challenge. Through 2000 and 2001 their results improved as the Focus WRC became more competitive, finishing second in the drivers' standings in 2001 just two points behind Richard Burns. In 2002, their final year together, Grist and McRae took four consecutive wins at the Acropolis Rally and won the last-ever Safari Rally on its 50th anniversary, before personal disagreements led to their split after the Rally New Zealand. Derek Ringer, McRae's earlier co-driver, completed the 2002 season.
In total, Grist and McRae won 17 rallies together and recorded 27 podium finishes.
In 1998, while racing with McRae, Codemasters developed the Colin McRae Rally game for PlayStation and Windows, in which Grist lent his voice and likeness as co-driver. His pace note calls — direct, clipped, and timed — became familiar to a generation of sim-racing fans. He appeared in subsequent games through Colin McRae Rally 2005. Archive recordings were also used in the 2013 mobile version, and Grist reprised his role as one of the default co-drivers in Dirt 4.
In 2003 Grist moved into television, working as a presenter for Speed TV in the United States and contributing to the worldwide WRC review programme. He rejoined McRae occasionally for one-off events, including the 2005 Rally GB and Rally Australia in a Skoda, and competed with him at X Games 12 in Los Angeles in 2006, where they narrowly finished behind Travis Pastrana.
McRae's last WRC appearance with Grist was at the 2006 Rally of Turkey. On 15 September 2007, McRae died in a helicopter crash near his home in Lanark, Scotland.
In 2006 Grist founded Nicky Grist Motorsport, initially as the sole UK distributor of Stilo helmets, expanding into a full motorsport equipment retailer based near Pontrilas, Herefordshire. He has also served as an informal safety consultant to the FIA WRC on helmet and HANS device regulations.
Grist married Sharon in 1993, during the recce for Rally Portugal, in Abergavenny, Wales. In 2019, he participated in the non-competitive Eifel Rallye Festival as a driver in his Celica GT4 ST185.