Use Catalog Prices

Shopify Catalogs allow you to specify different prices for products based on location. When this is enabled the app will use your catalog prices based on the location.

Once this feature is enabled the app will use prices based on the Catalog price for the selected location.

What if I only have 1 market and 1 catalog?

Shopify let's you create multiple sub markets under a market https://help.shopify.com/en/manual/markets/getting-started/submarkets

So for example, if you already have a Singapore market you should be able create a West Singapore submarket. Then you can create a new Location inside that location to use that catalog. When it is done you should have

"West Singapore" Location → "West Singapore" Catalog → "West Singapore" market

I hope that makes sense!  I'm sorry this is a little complicated. I think when Shopify built catalogs they wanted to use it to target different geographical regions. Hopefully Shopify will make it easier in the future.