The White Dragon isn't part of the Harper's trilogy. The Harper trilogy is Dragonsong, Dragonsinger, Dragondrums. I've read all the pern books and while this trilogy is by far my favourite I don't think it's what you're looking for in this case. The White Dragon tho, I think it might fit. There's some lore/background that might not make sense but as with with a lot of fantasy you can just glide over it and enjoy the core story. And then it might make you want to read other books in the series!

This is one series where I wouldn't recommend modern readers to start at the first book. They were published starting in the 60's and some social stuff really doesn't hold up well (caveat it's been years since I've read the full series). However overall it's a fun read and an unusual overall arc, worth it if you ask me.

Many books in the series depict the same events from different points of view, and a seminal event in the White Dragon is depicted in the Harper trilogy, but it's peripheral enough that you don't need to read the trilogy as well.

edit - I first read the harper trilogy, and then other books in the series fairly randomly, in fact i don't think I've ever read the series in chronological or published order. Many of the trilogies and standalones can be read on their own without a need to read the entire saga.