Neil-Smith attended Wilkins Public School in Marrickville and Newington College in Stanmore where he joined the school's 1st XI cricket team aged 14 in the year they went on to win the GPS[7] Premiership. He was in the Cricket NSW pathways program 2012-2018 and was a Cricket NSW Basil Sellers Scholarship recipient in 2017.[8] He was also a talented AFL player and was a member of the Sydney Swans Academy from 2010 to 2015.
He was part of the New South Wales squad at the U19 National Championships in 2016 and 2017[9] and was the competition's 3rd highest and 2nd highest wicket taker respectively. NSW won the championship in 2017.[10] In 2018 he was selected in a 28-man provisional Australian squad for the U19 Cricket World Cup but missed out on the final squad. He was selected in a U19 Australia squad to play in an ODI series against the U19 Pakistan team in Melbourne.[11] His first grade team in NSW was the Sydney University Cricket Club (cap no. 757) and in Tasmania he plays for Clarence District Cricket Club.
Neil-Smith made his first-class debut against WA at the WACA on 10 October 2019 which ended in a draw. He took 3/81 off 17 overs in the first innings and 2/90 in the second innings.[12] Batting in the first innings he finished 39 not out off 150 balls and the 111-run stand, which he shared with Australian Cricket Captain Tim Paine, who claimed his second first-class century[13] became the highest ninth wicket stand at the WACA.
In October 2021, during the 2021–22 Sheffield Shield season, Neil-Smith took his maiden five-wicket haul in first-class cricket, with 5/43 against Western Australia,[14] he also scored 60 runs and was named man of the match.[15] In season 2022-23 he took his best figures against NSW at the SCG claiming 7/58 and 3/46.[16]