Hong Kong terminal 1 lounge access

Premium economy does not provide lounge access, from what I see on Cathay Pacific site.

I could not find what it would cost , or even if, a day pass can be purchased.

I would call the airline to inquire about the what and how of buying a day pass

You can always inquire at one of the Cathay lounges upon arrival to see if they accept walk-ins (for a fee).
Failing that there are commercial lounges : https://www.plazapremiumlounge.com/en-uk that cater to transit passengers not otherwise elegible for airline lounge access. They're not cheap - typically USD$75 for 2 people for 2 hours - but they are quite nice, and include shower facilities if you'd like to freshen up before proceeding on.

hey hey pip
check out loungebuddy.com put in your airport to see if it's listed and go from there.
different packages for how many hours and what amenities are included. read the reviews, do you want before or after security, some may have restrictions like what gates are available to enter. read all instructions and rules.
check prioritypass.com different "class" offers with an annual fee.
loungepass.com is another site. we are using this one when we depart Paris (CDG).
groupon.com if you've heard of it or use it, sometimes they may have a special 2 for 1. i found one for oakland, ca airport (OAK). read again, expires in 120 days so don't buy too early.

good luck
aloha

While it doesn’t have any food or drink, there is a free lounge with flat beds for passengers flying on any airline in terminal one. First come first serve. The airport website will give you the location.