Han Solo's early days are on display in the new film Solo: A Star Wars Story, as the movie shows what the scruffy-looking nerf herder was up to before he met Luke and Leia in the original Star Wars film, A New Hope. Solo depicts the beginnings of Han's time as a smuggler, and alludes to his work with infamous gangster Jabba the Hutt, for whom he is already working in A New Hope. But what did Han Solo do for Jabba the Hutt before A New Hope? Mild spoilers ahead for Solo.
Jabba the Hutt doesn't appear in Solo, in fact, he's not even mentioned by name in the film. However, someone who sounds quite a bit like Jabba is heavily hinted at as someone for whom Han will soon go to work, and if you read between the lines it's not hard to figure out that the movie is alluding to Han's partnership with Jabba as seen in A New Hope. In that film, the pair's work relationship is already established. Han is first introduced in Mos Eisley Cantina, where he is soon seen having a discussion with the bounty hunter Greedo about money he owes Jabba after he dropped some smuggled goods when his ship was boarded by Imperial officers. That's as close as the original films ever get to unveiling the work Han did for Jabba, so for more details, fans traditionally looked to the now-defunct Expanded Universe.
Star Wars has always had a massive and passionate fanbase, but for many years, there were no new movies to placate these fans. After the original trilogy concluded with Return of the Jedi in 1983, there wouldn't be another Star Wars film until 1999's The Phantom Menace, leaving fans in the dark for 16 years. But even though there weren't any new movies during that time period, there was still a ton of canonical Star Wars content in the form of what became known as the Star Wars Expanded Universe, which consisted of role playing games, comic books, and most importantly, novels.
The Expanded Universe novels actually began before the original trilogy concluded, with 1978's Splinter of the Mind's Eye taking place between 1977's A New Hope and 1980's The Empire Strikes Back. The first attempt to tell Han's backstory came in author Brian Daley's "Han Solo Adventures" trilogy of novels, published between 1979 and 1980: Han Solo at Stars' End, Han Solo's Revenge, and Han Solo and the Lost Legacy. However, it wasn't until Ann C. Crispin's "Han Solo Trilogy" that the smuggler's relationship with Jabba the Hutt was revealed. Those books were published from 1997 to 1998 and consisting of The Paradise Snare, The Hutt Gambit, and Rebel Dawn. And it's in this last book that Han's relationship with Jabba is revealed.
In Rebel Dawn, which takes place right before A New Hope, Han and Chewie are in need of some funds, so they take a job from Jabba running spice — an illegal drug in the Star Wars Expanded Universe — from the mines of Kessel. This takes them through the infamous Kessel Run, where they are forced to drop the spice after being pursued by Imperial forces. Jabba then demands Han pay for the lost cargo, which sets up Han's face off with Greedo in Mos Eisley. However, it seems unlikely that this relationship between Han and Jabba is still canon.
When Disney purchased Lucasfilm in 2012, they declared that the Expanded Universe was no longer canon, and would henceforth be known as "Star Wars Legends." Under the new guidelines, only the movies, current TV shows, and materials published after 2014 would now be considered Star Wars canon. Under this new canon, Han Solo is shown working as a smuggler for Jabba the Hutt in some of the new Star Wars comic books from Marvel Comics, but the stories don't go into much detail about the nature of his smuggling, and it seems unlikely that family-friendly Disney will show him once again as essentially being a drug dealer.
With the Star Wars canon reset, much of Han Solo's established backstory is no longer considered to have actually happened, meaning there's no definitive answer as to what type of work Han was doing for Jabba before A New Hope. Other than smuggling some sort of illicit goods, that is.