A tough question, Chester is so large that you are bound to miss out somewhere. I've never used the zoo's app, because I know my way around so well: but I would recommend that you download the latest version (there were some problems with the previous one). Then I would study it with a mental list of the animals that are your top priorities, for example if you
really want to see the sifakas, you need to be able to have a second chance in case they don't show the first time. For that reason I would never recommend an inflexible itinerary, but here are some suggestions.
Try to arrive early; if you are driving aim to be at the zoo by 9.40. There is usually a long line of cars being directed into the car park and after parking it will take you a few minutes to get through the entrance formalities. If you can actually get into the zoo before 10am, you can wait between the elephant paddock and the Bembe Kitchen until they drop the rope across the path to let visitors into the zoo proper. If you are really early, you can get a coffee while you wait

I would recommend that you should first turn left past the elephants and head for the Realm of the Red Ape (RotRA) before it gets busy and a queue builds up, you'll get better views of the animals too. Then you can choose between the Aquarium and the flamingos in the new South American aviary and see the penguins and the giant otters too. I would certainly go through Dragons in Danger and the Madagascar area in the morning too - the lemurs tend to take a siesta around noon (remember that you
must wear a facemask if you go in the lemur walk-through).
I would allow plenty of time for Islands, there is so much to see there that you can't see anywhere else in the UK. I would suggest that you follow the proper one-way system, entering between the bongos and the sitatunga. The Lazy River boat ride is a nice relaxing extra, but there can be a long queue - ask the guide at the entrance before you decide.
I would leave the Tropical Realm until later in the afternoon, when it will be quieter and you are likely to get a good view of the tuatara. Don't forget to exit past aye-ayes and then you can go on to the jaguars.
Enjoy your day