I had an outline for a book series in which I introduce a new character in one of the later volume to act as an introductory viewpoint character for people who are just picking up the series for the first time. However, the character never really meshed well and I had been considering writing them out. I thought about why the character felt like they didn't mesh well, and I realized the problem was that the character takes away from the more interesting parts of the story. I.e., the volume allows for a lot of payoff for the character development that was seen in previous volumes and an evolution of the main protagonists' dynamics, but instead of seeing the fruition of the character's relationships and how they have grown the story shifts such that a character the audience has no investment in and by themselves don't care about seemingly hogs a disproportionate share of the spotlight.
The only character that I introduce later on is the child of some of the main characters, but in that case it seems to work a lot better because the existence of a child puts said characters in novel situations and stimulates novel and interesting reactions out of them. However, I don't know how to do this when parental relatedness isn't a factor.
I know this is a general problem with writing, in that readers often become attached to the first characters they see and are more suspicious of newer ones; that newer ones have to earn the audience's investment because they already have a stronger connection to the ones they've seen before. My question is how to do you introduce a new character to a story with an established cast dynamic without making it seem like you are shoehorning them in there and taking attention away from the characters the audience actually wants to see and is invested in?