Ace Ventura 3 never happened because Jim Carrey wasn't interested in making sequels at that point in his career. Ace Ventura: Pet Detective made Carrey a proper movie star in the mid-1990s, so it was surprising that a sequel to Ace Ventura: When Nature Calls wasn't made. Both films earned big money at the box office, and the focal star remained a bankable A-lister well into the early 2000s. But as it turns out, there are a few good reasons why Ace Ventura 3 was never made.
When Ace Ventura: Pet Detective initially released, Carrey was somewhat well-known for being a cast member on In Living Color. With his memorable celebrity impressions and knack for physical humor, the stand-up comedian then applied his skill set to the big screen, and immediately became a household name. Produced for just $15 million, Ace Ventura: Pet Detective topped $100 million theatrically, and paved the way for an inevitable sequel. Unsurprisingly, Ace Ventura: When Nature Calls had a bigger budget ($30 million), even though it wasn't necessarily better than the original film. Still, the sequel outperformed its production costs seven times over.
In retrospect, Carrey's filmography shows his willingness to evolve as a performer, so it's entirely possible that he simply wanted to move on from the Ace Ventura character. For example, the 2017 documentary Jim & Andy: The Great Beyond encapsulates that very idea, as Carrey discusses the experience of fully immersing himself into characters - most notably as Andy Kaufman in Man on the Moon (1999) - only to then separate himself completely. Carrey did return as Lloyd Christmas for Dumb and Dumber To (2014), a sequel to Dumb and Dumber (1994), but he's made it clear in recent years that he prefers to evolve as an artist, rather than reprise roles for the sake of nostalgia.
Logistics are another reason why Ace Ventura 3 was never made, as Carrey reportedly didn't have a positive experience on set for Ace Ventura: When Nature Calls (via Den of Geek). He fired the original director Tom DeCerchio and replaced him with screenwriter Steve Oedekerk. It's also been reported that Carrey was even zanier behind the scenes than he was on camera, which correlates with the on-set behavior shown later in Jim & Andy: The Great Beyond. So, if Jim Carrey isn't thrilled about revisiting past roles as a general rule, it's highly unlikely that he'd want to reprise a character that brings up bad memories.
Ace Ventura 3 was never made without Carrey, because such a film would seemingly be a disaster, or would at least devalue the franchise as a whole. Meaning, Carrey is Ace Ventura, and vice versa, so it doesn't make sense for any Hollywood star to do a cheap impression. Due to the physical nature of Carrey's performances in the first two films, he would theoretically need to channel that same energy for a successful third installment. Now, in 2020, it seems that Ace Ventura 3 will always be a "what if" movie, one that was never made because of timing and circumstances.