I have started a new game and as soon as I reach the start of the premier league season the home kits do not show for Liverpool, Arsenal and some others during matchday.

Please can someone assist with a solution to this problem? Thank you.

I think this is a known issue, found this readme file in the 3D version of the kits, info copied below for convenience:

Arsenal, Liverpool and few other kits won't be visible in some competitions if you don't use *.fmf editor data file that  is included in this pack.

The file should be unpacked in your ...documents/sports interactive/football manager 2021/editor data folder.

When starting new game, make sure the file is listed and selected in database selection menu (upper right corner).

Video of full installation: https://www.youtube.com/watch?v=unuu-itsJpE&t=40s

If you're already in career in progress and don't want to start new game, then in-game editor is required. In kits & color section, find shirt items, delete multiple entries and for the one and only that remains, make sure it's not assigned to any competition.