I was surprised at how few characters from the Phoenix Wright trilogy made appearances in Apollo Justice: Ace Attorney. Many of the most important characters from the first three games in the series don't appear at all in the new game, and a couple only make minor cameo appearances. In fact, only two major characters from the first series are still important in Apollo Justice: Phoenix Wright himself and the Judge. Noticeably missing are Miles Edgeworth, Franziska von Karma, Pearl Fey, and most notably Maya Fey. Instead of bringing back these old characters, it seems that the designers of the series chose to start over from scratch.
Honestly, I can't really say that they made a mistake in focusing on a brand new list of characters. By the end of Apollo Justice, I really liked most of the new main cast. Apollo, Trucy, and Klavier Gavin are all interesting and entertaining. Making the transition from Phoenix Wright to Apollo Justice as main character, and selling that transition to the fans, was the developers' hardest task in the game. If the developers had relied heavily on familiar faces from the first three games, it would have felt too much like Phoenix Wright was still the main character. That would have undercut Apollo's chances of being accepted. Instead, the developers created new characters to fill out familiar roles in the story.
Most of the new main characters in Apollo Justice are essentially replacements for the old Phoenix Wright characters. Ema Skye is replacing Detective Gumshoe, Klavier Gavin replaces Miles Edgeworth, and Trucy Wright replaces Maya Fey. However, since many of these characters have very different working relationships and interactions with Apollo than their originals did with Phoenix Wright, it helps to make them feel very different than the originals. Ema Skye's moody personality, love of forensic science, and general openness with Apollo are very different than Gumshoe's overall pathetic but good-natured personality and sometimes oppositional attitude towards Phoenix. Klavier Gavin is certainly more laid back than any of the Phoenix Wright prosecutors.
The only character who is somewhat problematic is Trucy. Admittably, part of my problem was that I incorrectly guessed that she was actually Pearl Fey based on promotional information. After all, Trucy was the same age Pearl would be, had the same hair and eye color, and had the same bouncy personality. So I was quite surprised to find out in the third case that she was most certainly not Pearl, but instead a completely new character. I was disappointed, since it meant that there wasn't a connection to the original story that I was expecting, and it meant that Trucy was simply an Expy of previous characters (Maya and Pearl). However, my opinion on the matter has reversed since I finished the last case. The revelation of Trucy's real connection to Apollo has put a fresh spin on the character concept that I like.
At this point, my only complaint about the characters in Apollo Justice is that Apollo Justice himself sounds too much like Phoenix Wright during investigation phases. During trials, Apollo feels like a very different character because of his distinctive expressions, special power, and favorite sayings (Phoenix wouldn't be caught dead saying "Here comes Justice"). However, his narrative voice and thoughts while examining objects and evidence use the exact same brand of humor that Phoenix used in the in original series. Apollo just doesn't feel different enough. It might have been better if he was more foolishly optimistic than dry and sarcastic like Phoenix was.
Anyways, now that the first Apollo Justice game has fully established Apollo and the rest of the new cast, I expect the second game to bring back more characters from the first three games. A big part of the fun factor of a time jump is seeing what has happened to familiar faces during the intervening time period. I would be very disappointed if there was no resolution to that.