2016: two-year-old season

On 11 September, at Hanshin Racecourse, Suave Richard began his racing career by finishing second to Meliora in a 2000 metres contest for previously unraced juveniles. Three weeks later, he recorded his first victory when he won a maiden race over the same course and distance.^[6] On 19 November, he was stepped up in class for the Grade 3 Tokyo Sports Hai Nisai Stakes over 1800 metres at Tokyo Racecourse when he started at odds of 7.1/1 and finished second, beaten a neck by Bless Journey.^[7]

In the official Japanese rankings for 2016, Suave Richard was rated the fifth-best two-year-old colt, four pounds behind the top-rated Satono Ares.^[8]

2017: three-year-old season

Suave Richard's trainer Yasushi Shono

Suave Richard made his three-year-old debut in the Tokinominoru Kinen (a trial race for the Satsuki Sho) over 1800 metres at Tokyo on 12 February and started the 2.1/1 second favourite. Ridden by Hirofumi Shii he settled behind the leaders before staying on in the straight, taking the lead in the last 200 metres and drawing away to win by two and a half lengths from Etre Digne.^[9] In the 77th running of the Satsuki Sho at Nakayama Racecourse on 26 April he started second choice in the betting but although he finished strongly he was never able to reach the leaders and came home sixth behind Al Ain.^[10] He was then moved up in distance for the Tokyo Yushun over 2400 metres at Tokyo on 26 May in which he again made good late progress but failed by three-quarters of a length to reel in the winner Rey de Oro.^[11]

After a break of over five months, Suave Richard returned in the Grade 2 Copa Republica Argentina over 2500 metres at Tokyo, a race in which he was matched against older horses for the first time and ridden by Mirco Demuro, who became his regular jockey. After racing in mid division, he moved up on the inside entering the straight, gained the advantage 300 metres out and quickly broke clear of the field to win by two and a half lengths from the five-year-old Sole Impact.^[12] On his final run of the season, the colt contested the Arima Kinen at Nakayama on 24 December and came home fourth of the sixteen runners behind Kitasan Black, Queens Ring and Cheval Grand.^[13]

In the 2017 World's Best Racehorse Rankings, Suave Richard was given a rating of 118, making him rated the 90th best horse in the world and the seventh-best horse in Japan.^[14]

2018: four-year-old season

Mirco Demuro who rode Suave Richard in 2018

2018 Osaka Hai Awards Ceremony

On his first run as a four-year-old, Suave Richard started odds-on favourite for the Grade 2 Kinko Sho at Chukyo Racecourse over 2000 metres on 11 March. After tracking the front-running outsider Satono Noblesse for most of the way, he took the lead in the closing stages and won by half a length, with Satono Diamond a length away in third place.^[15] Three weeks later, the colt contested the Grade 1 Osaka Hai over the same distance at Hanshin and went off the 2.5/1 favourite in a sixteen-runner field which also included Al Ain, Satono Diamond, Cheval Grand, and the Mile Championship winner Persian Knight. Suave Richard raced towards the rear in the early stages before rushing up on the outside to dispute the lead in the straight. He gained a clear advantage early in the straight and "romped to a convincing victory", holding off the late charge of Persian Knight by three quarters of a length. Mirco Demuro commented "Since the pace was very slow, I decided to make an early bid. He responded so well, I had absolutely no doubts in him and he stretched beautifully".^[16] In June, the colt was dropped back in distance for the Yasuda Kinen over 1600 metres and started favourite, but after challenging for the lead in the straight he was outpaced in the final strides and came home third behind Mozu Ascot and Aerolithe, beaten a neck and three quarters of a length.

Returning from a lengthy summer break, Suave Richard was made favourite for the autumn edition of the Tenno Sho at Tokyo on 28 October, but after being badly hampered shortly after the start, he was never in serious contention and finished tenth behind Rey de Oro.^[17] The colt ended his season in the Japan Cup at Tokyo on 25 November in which he started the 5.5/1 second favourite and finished third behind Almond Eye and the front-running Kiseki.

In the 2018 World's Best Racehorse Rankings, Suave Richard's rating of 121 made him the thirty first best racehorse in world.^[18]

2019: five-year-old season

Suave Richard began his fourth campaign in the Nakayama Kinen over 1800 metres on 24 February when he stayed on well without being able to reach the leaders and came home fourth behind Win Bright, Lucky Lilac, and Stelvio. Rather than attempt a repeat victory in the Osaka Hai, the horse was sent to the United Arab Emirates to contest the Dubai Sheema Classic at Meydan Racecourse on 30 March. Ridden by João Moreira, he was restrained at the rear of the field before finishing strongly to take third place behind Old Persian and Cheval Grand. On his return to Japan, he went off the 7.8/1 sixth choice in the betting for the Takarazuka Kinen over 2200 metres on 23 June at Hanshin. The horse finished the race at third place behind Lys Gracieux and Kiseki after racing on the wide outside for most of the way before keeping on well in the straight.^[19]

On his return in autumn, Suave Richard was partnered by Norihiro Yokoyama when he made his second bid for the Tenno Sho. He raced in mid-division before making some progress in the straight but never looked likely to win and came home seventh behind Almond Eye, beaten five and a half lengths by the winner. On 24 November Suave Richard was one of fifteen horses to contest the 39th running of the Japan Cup and started the 4.1/1 third choice in the betting behind Rey de Oro and Wagnerian. The other contenders included Makahiki and Cheval Grand in a field which, for the first time, contained no overseas challengers. Ridden by Oisin Murphy he raced in mid-division he made a forward move on the inside entering the straight, gained the advantage 200 metres from the finish and held off the challenge of the three-year-old filly Curren Bouquetd'Or to win by three quarters of a length.^[20] Commenting on his decision to launch his final challenge along the inside rail Murphy said "I had the option of forcing Curren Bouquetd'or out. I could have done that. He's a big enough horse. But that would have taken too much energy, so I took the shortest way... I knew for the last 200 meters that Suave Richard would win" while Yasushi Shono said "both the horse and the jockey had a lot of courage".^[21]

Suave Richard ended his season on 22 December with a second attempt to win the Arima Kinen. He started at odds of 16.5/1 and was never in serious contention before finishing twelfth of the sixteen runners behind Lys Gracieux.^[22]

In January 2020, at the JRA Awards for 2019, Suave Richard finished third to Win Bright and Indy Champ in the poll to determine Best Older Male Horse.^[23] In the 2019 World's Best Racehorse Rankings Suave Richard was given a rating of 121, making him the 29th best racehorse in the world.^[24] Later that same month, it was announced by Shono that, in spite of the horse being selected for that year's Dubai Sheema Classic, the horse would be retired to stud due to his right hock becoming swollen not long after his last race.^[25]