2000: two-year-old season

On 14 June Beckett began his racing career in a maiden race over six furlongs at Leopardstown Racecourse in which he started the 2/5 favourite and won "comfortably" by one and a half lengths from America Calling after leading from the start.^[5] The colt was moved up in class for the Group 3 Futurity Stakes over seven furlongs at the Curragh in August in which he was made the 6/1 fourth choice in the betting in a seven-runner field headed by his more fancied stablemate Bonnard. Ridden by Seamie Heffernan, he tracked the leaders before taking the lead a furlong out but was overtaken in the final tride and finished third, beate half a length and a short head by Lady Lahar and Bonnard.

On 17 September the colt was ridden by Heffernan again when he stepped up to Group 1 level for the National Stakes on yielding ground over the same course and distance. His stablemate Darwin started the 4/9 favourite ahead of Down To The Woods and Bonnard with Beckett next in the betting on 10/1. The other five runners included King's County (yet another O'Brien trainee), Berlin (third in the Anglesey Stakes) and the Dermot Weld-trained Elbader. Heffernan positioned the colt just behind the leaders as Down To The Woods set the early pace from King's County, but began to make progress two furlongs from the finish. Beckett went to the front approaching the final furlong and drew away in the closing stages to win by three lengths from King's County with the outsider March King staying on to take third.^[6] After the race Aidan O'Brien said "I think Beckett is a potential 2,000 Guineas horse. He's a lovely mover but he was able to handle the ground this time. He's got a great pedigree... You can't beat blood",^[7] while Heffernan commented "Beckett loved the ground. He relaxed very well for me and then picked up nicely when I said go".^[8]

2001: three-year-old season

Training problems kept Beckett off the racecourse for the spring and summer of 2001. After an absence of a year he returned in the Listed Solonaway Stakes over one mile at the Curragh on 15 September. Starting the 7/4 favourite he took the lead approaching the last quarter mile but was overtaken inside the final furlong and beaten a head by Magic Cove. On 4 October the colt was sent to England and was made 3/1 favourite for the Joel Stakes at Newmarket Racecourse where his opponents included Malhub, Swallow Flight (Royal Windsor Stakes),Priors Lodge (City of York Stakes) and Lincoln Dancer (Sandy Lane Stakes). Ridden by Mick Kinane, he took the lead from the start and was ever headed, staying on well in the closing stages to win by three quarters of a length from Priors Lodge.^[9] Aidan O'Brien commented "the plan was to come here and then return for the Champion Stakes. That remains the same. He gets a mile really well and I think a lot of him".^[10] Sixteen days later at the same track, Beckett returned to Group 1 level for the Champion Stakes, as O'Brien had predicted. He led for the first seven furlongs before dropping out of contention and finishing tenth of the twelve runners in a race won by Nayef.