You have two choices - you can either keep them on you Citi Premier Miles card and transfer them when you need them (you could also transfer to Thai Royal Orchid, NorthWest WorldPerks, or Krisflyer), or alternatively you can sign up for auto-transfer, which will do it automatically like on the old card. The advantage of not doing it automatically is that the miles never expire while they are on your Citi card, but once you transfer them to AsiaMiles they expire after 3 years.
I think you make be confusing Priority Pass with access to the Plaza Premier lounges at HK airport. Most platinum cards in HK have access to the Plaza Premier lounge. Far fewer have Priority Pass membership.