Tommy started out in motor sport in a Mini in the mid 1970s competing in local rallies but after a crash it seemed that his desire to go racing would go no further. However a trip to Mondello Park to the Racing School rekindled his enthusiasm.
Early in 1977 he bought a Crosslé 20F Formula Ford and entered a few races with no results. Tommy went back to the Mondello Park Racing Driver School where John Murphy spotted his raw talent. He entered Tommy into the Formula Ford Festival at Brands Hatch late in 1977. Byrne drove a Royale RP21 and impressed, however a spin ruined any chance of reaching the final.
In 1978 he continued in Formula Ford with a Hawke DL17/19 was bought however no results were forthcoming until he switched to a PRS RH01/78F. He put the PRS on pole and won the first time out.
In 1979 he got the works drive with the PRS team. Byrne had a rough season. Trying too hard caused him to have too many 'offs'.
1980 saw Tommy return to the front in a Van Diemen RF81, finishing second in the Formula Ford Festival.
In 1981 he moved to FF2000 due to a lack of budget to do F3. He won the British and European titles and stood in for Ayrton Senna at the Formula Ford Festival and won.
Then, after choosing to do British F3 with Murray Taylor Racing for 1982 his career really took off. Taking seven wins and the Marlboro F3 title due mainly to his stunning early-season form in Taylor's Ralt-Toyota RT3.
During the year he was offered a job with the new McLaren International team as their test driver. Tommy turned down their offer to take a race seat at Theodore. Three DNQs and two starts from the final grid position were all he had to show for his F1 career though ironically he won a test with McLaren as part of his prize for winning the F3 Championship. In the test he set the third fastest ground-effect time ever recorded at Silverstone.
The Silverstone test didn't open any doors in F1, so Byrne joined Eddie Jordan Racing for the European F3 championship. He won two rounds and finishing fourth in the overall ranking. At the end of the season Tommy switched to the works Anson Alfa Romeo SA4B.
1984 saw Byrne still in F3 for another attempt at the European title, again driving for the Anson team. He finished 6th in the Championship.
In 1985 Tommy turned to North America, driving in the American Racing Series. In 1988 Tommy nearly returned to the front line but just lost out on the ARS title by three points to Jon Beekhuis. He won three races and led for 114 laps, but a missed race at Milwaukee and a mid-season switch of teams damaged his efforts.
He finished second again in 1989. The next year Byrne took just one win at Detroit. Byrne finished outside the top ten.
After a season in Mexican F3 Tommy retired though he has recently competed in the Grand-Am series in a Porsche 911 GT3-R.
He now lives in the US and works as a racing instructor.