Although Brad Smith was born in the Australian state of New South Wales, he moved to England in his early teens and was spotted by Liverpool scouts while playing for the same school as fellow defender Jack Robinson, his senior by seven months. Jack made his first senior appearance for the club in the final match Rafa Benítez took charge of in May 2010. Robinson was only sixteen years old at that time and Smith, who had reached his own sixteenth birthday exactly a month before Robinson made that debut at Hull City, was quickly moved up from Liverpool’s Under 16 team and became a regular for the Under 18 team in the 2010/11 season. Good form for his club was recognised at international level and he went with England to the Under-17 European championships held in Serbia during May 2011. Smith scored in a group-match victory against the host country but England were knocked out by the Netherlands in the semi-final.
The lightning quick left-back moved up to the club’s reserve team for the 2011/12 season and he impressed enough there to be one of the young players taken by incoming manager Brendan Rodgers on the North American tour in the summer of 2012, where he was named as one of the substitutes for the second match against Roma at Fenway Park, Boston. Back in England his 2012/13 season with the Under 21 team was disrupted by a bad knee ligament injury and he was out for almost a full year. On his return to action he immediately started to play with the assurance and composure he had shown before his injury, was rewarded by being given a first-team squad number (44) and was named as one of the substitutes for the first team’s Boxing Day match at Manchester City as 2013 drew to a close. Although not called on that evening, he made his debut three days later (against Chelsea at Stamford Bridge) and also made the senior match-day squad when Everton came to Anfield at the end of January.
As the 2013/14 domestic season closed, Smith was named in Gareth Southgate's Under-21 squad ahead of an important European Championship qualifier against Wales which would be followed by the Toulon Tournament in France where England would meet Qatar, Brazil, South Korea and Colombia in quick succession. Before that sequence of international matches began Smith was included in the Liverpool squad that travelled to Dublin to play Shamrock Rovers in a post-season friendly match at the Aviva Stadium. Brad was one of only five Liverpool players to play in the whole match and he impressed hugely to again confirm that he has a bright future in the game. Smith played in 16 Under-21 matches for Liverpool in 2013/14, scoring twice (against Arsenal and Tottenham).
In the Toulon Tournament of 2014 Smith made a 15-minute substitute appearance as England beat Qatar 3-0, had 30 minutes as a substitute in the 2-1 defeat by Brazil, played from the start but was taken off shortly before half-time in the 1-1 draw with South Korea and was an unused substitute for the 1-1 draw against Columbia. England qualified for the 3rd/4th place play-off match against Portugal on 1 June. Portugal won 1-0 but Smith remained on the substitutes' bench for the whole match. Smith went on youth loan to Swindon Town on 8 August 2014. After playing in seven League One matches for Swindon at the start of the 2014/15 season Smith was recalled to Liverpool on the 20th of October.
Smith made his full international debut for the country of his birth, Australia, in a friendly on 4 September 2014. "I’d like to thank all the England coaches for what they've done for me throughout the youth level but it was always a dream for me and my family to play for Australia," Brad told Sky Sports. "That’s where I was always going to go. I was born in Penrith and moved around Byron Bay. Dad lives in Forster Tuncurry. It was a big decision for all of us but it was the right one."
At the end of 2014/15 Smith was offered a new contract by the club, but his representatives rejected this believing he could get more money and playing time elsewhere. As he was under 24 though the Reds were able to hold on to his registration and demand a fee set by tribunal should he sign for somebody else. With no offers forthcoming as interested clubs could not know what the fee would be, he had a change of heart and a new deal was signed in November. On 2nd December he came off the bench with thirteen minutes remaining to set up the final goal in the 6-1 rout of Southampton in the League Cup. He then started the Europa League game in Switzerland against Sion and came off the bench against West Ham in the league. He started the FA Cup third round tie at Exeter, getting his first goal for the Reds when he equalised in the 73rd minute. Although a regular on the bench for the rest of the season, his only three further league appearances were when Jurgen Klopp made wholesale changes ahead of Europa League ties. On 27th July 2016 he signed a four year deal with Bournemouth after Liverpool let him go for a reported £3 million fee.
Smith failed to establish himself in the side there, making only ten appearances in two seasons and on 8th August 2018 was loaned to MLS side Seattle Sounders. He appeared six times in the MLS, but was then ruled out for the rest of the campaign with a muscle injury. 2019 started better for him however and he earned a first call up the Australia side in nearly two years, playing against South Korea in a friendly in June. He remained on loan with Sounders until December, ending the season as an MLS Cup winner. On 30th January 2020 joined Championship side Cardiff City on loan for the remainder of the season. He made just three substitute appearances, all coming in the last ten minutes of games. In September 2020, his Bournemouth contract having expired, he re-joined Sounders and helped them to the MLS Cup final, where they were beaten 3-0 by Columbus Crew.