This trophy is won at the war table, you will eventually get a quest to gather coin, well there is a trick to the table that you can advance time for all the quests by going in to the PS4 settings and advancing the time manually.
The video will show you how to do this quickly.
I guess this method could be used to quickly farm money, herbs and metals with the gather herbs and metal quests on the war table also if you wish to.
I personally was not sure how to upgrade the throne and when finding this video realised you get it just by doing the quest at the war table and once you get the parts it will pop. So don't worry about doing anything else like when you upgrade the gardens or towers you need to go look around Skyhold to make the changes, you don't need to do anything at all, like i say it will pop as soon as you open the quest report as long as you got the parts needed.
So just follow the steps on the video and you will eventually get the parts and with it the trophy. Don't worry if you don't get the parts straight away you can just keep using the method shown on the video repeatedly until you do so.
If you don't want to use this as a way to advance other quests and wish to play them at the normal time rate just wait until all other war table quests are finished and then just use the gather coin quest alone.
Or if you don't want to use this method at all you just can just keep doing the gather coin quest at your own rate, it's entirely up to you.