The Victorian-born Bendigo Spirit guard made her WBNL debut with the Australian Institute of Sport (AIS) in 2009 after accepting a basketball scholarship she received through a national talent identification program.
In the same year, she made her international debut when she represented Australia as point guard at the first FIBA Oceania Under-16’s Championship, against New Zealand.
She travelled to France in 2010 with the Australian team for the Under-17s World Championships, where they were knocked out in the quarter-finals by the host country. In 2014, she was a member of the bronze-winning Australian team, losing to the USA team who would go on to win gold.
She spent three years with the AIS, before heading over to the Canberra Capitals for two more years, before signing with the Bendigo Spirit in 2013. The Spirit were back-to-back WNBL Champions in the 2012/13 and 2013/14 seasons.
She played forty-one games across two seasons there, before being recruited to Perth Lynx, where she was named captain. In 2019 Lavey returned to Bendigo.
Lavey was a part of the Rio 2016 basketball team, that was knocked out of the quarter finals by Serbia in a nail-biting 73-71 loss.
Tessa represented Australia at her first Commonwealth Games on the Gold Coast in 2018, where the Opals won gold in front of a home crowd. They thrashing England in the final, 99-55.
Later that year, Lavey travelled to Spain with the Opals for the 2018 FIBA World Cup, where they finished with a silver medal, losing the final to ten-time winners USA, 73-56.
In mid-2020, Lavey began training with the AFL Richmond Tigers, and was drafted to the team as the 43rd overall pick in the 2020 draft.