"The
Firm" is the name of three completely unrelated
music projects, apparently none of whom made a big enough
splash for their name to be remembered.
Chronologically, the first was a 1980s "supergroup" consisting of Jimmy Page of Led Zeppelin, Paul Rodgers of Free and Bad Company, Chris Slade of Manfred Mann, and Tony Franklin. They released two albums, 1985's "The Firm" which produced the hit single "Radioactive," and 1986's "Mean Business." After that they broke up; Page and Rogers continued to do solo albums, Franklin was later in hard-rock group Blue Murder, and Slade ended up in AC/DC.
The second group called "The Firm" were a comedy group led by John O'Connor of the new age group EKO; they released the album "Serious Fun" in 1987. They are mostly known for the song "Star Trekkin'," which is a classic for Dr. Demento listeners and those of similar tastes.
The third assemblage to use the name was made up of rappers Nas, Foxy Brown, A.Z. and Nature, who released the one-off album "The Album" in 1997. All of those musicians have released solo work since.
Source: Various articles under the group name at allmusic.com