In the early 1970s, Aldridge began playing original music with Alley Keith in the Florida Panhandle. Inspired by drummers such as Louis Bellson and Sam Woodyard, he started using a double-bass setup and became an early pioneer of the hard rock double-bass style of drumming. He soon gained notability as the drummer of southern rock group Black Oak Arkansas, recording several albums with the band between 1972 and 1976. Not happy with the band's heavy use of hashish, Aldridge attempted to leave. He was forced to sneak away in the middle of the night and subsequently "hide out in Chicago" upon leaving Black Oak Arkansas, as the band's management wasn't keen on giving him his contractual freedom. One and a half years of lawsuits ensued, after which he was free to record again. Aldridge then spent 1978 to 1981 with the Pat Travers Band, recording five albums over that time.
Upon parting ways with Travers in 1981, Aldridge moved to the UK where he began working with Gary Moore, recording the Dirty Fingers album in 1981. Through Moore he met guitarist Randy Rhoads and eventually joined him in Ozzy Osbourne's band. Although Aldridge is credited in the liner notes and pictured on the inner sleeve of Osbourne's 1981 album Diary of a Madman, Lee Kerslake actually performed all the drum parts on the original release. Aldridge has stated that working with Rhoads in Osbourne's band was one of the "musical highlights" of his life. Rhoads stated of Aldridge in late 1981 that "he was always my favorite drummer", stating that he was "knocked out" by the drummer after seeing him perform with Black Oak Arkansas on television in the 1970s. Aldridge appeared on Osbourne's Bark at the Moon album in 1983 as well as a pair of live albums (Speak of the Devil and Tribute) before leaving the band in 1983.
Soon after, Aldridge, along with bassist and former Ozzy Osbourne-bandmate Rudy Sarzo, joined forces with guitar/keyboard virtuoso Tony MacAlpine to form a short-lived project called MARS. Close friends, Aldridge and Sarzo then both joined Whitesnake, a band who were then touring in support of the highly successful Whitesnake album. Aldridge and Sarzo then performed on the band's follow-up album, Slip of the Tongue, released in 1989. Announcing he was going to take a break from the music industry, Whitesnake frontman David Coverdale put the band on indefinite hiatus after the tour.
Following his stint in Whitesnake, Aldridge played in the band Manic Eden, with his former Whitesnake bandmates Adrian Vandenberg and Sarzo. The line-up also included former Little Caesar vocalist Ron Young.
From 2007 to 2009, Aldridge was touring with Thin Lizzy alongside Scott Gorham, John Sykes and Marco Mendoza. The latter part of his drum solo in this Thin Lizzy tour includes a "hands-only" percussion piece where he plays snare, tomtoms, and cymbals without sticks as he also did while touring with Black Oak Arkansas, Pat Travers, Ozzy Osbourne and Whitesnake.
Tommy has been an in demand drum clinician since the early 1980s, and no matter who he works with, much of his work involves drum clinics and festivals each year. Aldridge plays Yamaha drums, a company he has been with since 1982. Yamaha has made Tommy a custom "soon to be released" Signature Snare drum that is a 7x14 Stainless Steel model with die cast hoops and black chrome hardware. He also endorses Paiste cymbals. His cymbal selection can vary, but he strongly prefers the brighter sounds of the 2002, Signature and RUDE cymbals that they offer.
It had been announced that Thin Lizzy, along with The Answer, were to support AC/DC at stadium shows in England, Ireland and Scotland at the end of June 2009, but these appearances were cancelled after Aldridge broke his collarbone in an accident. On June 30, the band's website announced that John Sykes had left Thin Lizzy and all shows for the rest of 2009 were cancelled or postponed. Gorham has stated that he will announce Thin Lizzy's future plans shortly. In May 2010 Thin Lizzy did not include Aldridge in the new line up, due to healing process from an injury and original drummer Brian Downey returning.
On January 25, 2013, it was announced that Tommy had rejoined his former band Whitesnake for the third time and is their drummer to this day.