Born in Penrith in Australia, Smith moved to England at the age of 14. While playing for his local high school side Smith was scouted by Liverpool and invited to join their academy.
Liverpool
A week before his debut, Smith was promoted to the first team alongside his U21 youth team partner Jordan Rossiter. On 26 December 2013, Smith was named on the Liverpool bench in a 2–1 loss at Manchester City. Three days later, he made his senior debut for Liverpool after coming on in the 59th minute, replacing the injured Joe Allen in a match against Chelsea at Stamford Bridge. He was deployed as a left winger, but was unable to make a difference to the result as Liverpool lost the match 2–1.
Loan to Swindon Town
On 7 August 2014, Smith was loaned to Swindon Town of League One on a season-long youth loan. He made his debut for the club two days later, playing the entirety of a 3–1 win over Scunthorpe United at the County Ground. He was recalled by Liverpool on 20 October due to a contract dispute, having played ten matches in total.
Return to Liverpool
In June 2015, Smith's contract expired with the player having rejected a new deal from the club however the club continued to hold his registration and as the player was under the age of 24, Liverpool would have been due a compensation fee if he had signed for another club. On 17 November 2015, Smith signed a new long-term contract with Liverpool, putting an end to his contract dispute. On 2 December, he came on as a 77th-minute substitute for Alberto Moreno in a League Cup quarter-final away to Southampton, assisting Divock Origi's hat-trick goal which confirmed a 6–1 victory. On 8 January 2016, he started his first FA Cup match for the club in a third round match against Exeter City and scored his first senior goal for the club. In the replay of the FA Cup match against Exeter City, Smith assisted the first goal, scored by Joe Allen, in the 9th minute. Smith made his first Premier League start against AFC Bournemouth on 16 April 2016 in a 2–0 victory for his side. He made his second Premier League start on 1 May against Swansea in a 3–1 loss, and was sent off for a second yellow card in the 76th minute.
AFC Bournemouth
On 23 July, it emerged that Liverpool had accepted an offer from Bournemouth for Smith, and the move was confirmed on 27 July, after he had flown back from Liverpool's pre-season tour of the US for a medical at the south coast club. A buy-back clause was included in the transfer agreement. Smith made his competitive debut for Bournemouth in a win over Morecambe in the 2016–17 EFL Cup on 24 August 2016. He then made his Premier League debut for the club on 27 November 2016 against Arsenal. He played 81 minutes as Bournemouth lost 3–1. It was not until Boxing Day that Brad Smith made his second league appearance for Bournemouth starting in its away match to Chelsea. Smith had only limited opportunities in his first season at Bournemouth, with Charlie Daniels preferred at left back.
On 8 August 2018, Smith was loaned to Seattle Sounders FC in Major League Soccer. Smith quickly became popular with Sounders supporters for his ability to get forward and combine with teammates, tallying 7 assists in 31 regular-season appearances. Smith was initially loaned to the Sounders for the duration of a year, with a return to Bournemouth set on 31 July 2019. However, the Sounders and Bournemouth agreed to extend the loan until the end of the 2019 MLS season. Smith started each game during the team's run in the 2019 MLS Cup Playoffs, helping the Sounders reach their third MLS Cup Final in four years. On 10 November 2019, Smith started in the 2019 MLS Cup Final, which the Sounders would win. Smith became the first Australian footballer to lift the MLS Cup trophy.
On 30 January 2020, Smith joined Championship side Cardiff City on loan for the remainder of the 2019–20 season.
International
Although he was born in Australia, Smith was also eligible to play for England as his parents are English. Smith represented the England under-17 side at the 2011 FIFA U-17 World Cup and made his England U20 debut at the end of the 2013–14 season. On 21 August 2014, Smith was named in the Socceroos squad to face Belgium and Saudi Arabia. He completed his change of eligibility to Australia against Belgium on 4 September 2014.
