Replace Polarizer on LG UltraFine 21.5" Display

My LG UltraFine 21.5” had a damaged polarizer. To fix it I got myself a new polarized, removed the old and applied the new one. With the new polarized the screen is actually worse than before. There are two things that went wrong:

1. dust particles and
2. air

caught between polarized and the screen. Air bubbles are highly visible on light images and dust particles on dark ones.

I was wondering if there is any particular technique to avoid those problems. So far I have only been working with screen protectors on screens as large as 10” and never had any issues but polarizers seem to be much more difficult as they use strong adhesive and any contact seems undoable.