First of all, I think some people misunderstand transparent addresses, aka t-addresses; t-addresses aren't inherently bad for privacy. The exchange from which you received your ZEC already has a transparent transaction record. Plus, most cryptocurrency (Bitcoin, Dogecoin, Ethereum, etc...) transactions are basically transparent, thus easily traced. And the moment you shield your balance the ZEC trail basically ends.
From that point on, a blockchain forensic analysis wouldn't know what happened to the coins that were once on the t-address.
Either way, it's good to know that there is a blockchain record of the flow of coins in and out of the t-address. In result, if you don't want people (other than the exchange) to know how many ZEC you have received and subsequently shielded, then you'll want to utilize the New Snap Address feature on Y Wallet.
Snap addresses, also called diversified addresses, are new addresses that you can use to receive ZEC, and are unlinkable.
With UTXO based blockchains it's generally a good practice to use a new receiving address for each transaction. The best part of new snap addresses is that people won't be able to parse them, to get your t-address history. It'll only show a new z-address if they try. Basically a snap address is just a fresh z-address disguised as a unified address.
Unified addresses are great, but not every exchange supports them yet. And Y wallet has unified addresses, but the default unified address can expose your Y Wallet's t-address history.
If you have a service, such as an exchange or wallet, that doesn't understand unified addresses (they're new), or it wont accept a unified address or z-address; then you will have to relinquish your t-address.
One way to extract your t-address and z-address from your unified address is to copy the following link text: https://zcashblockexplorer.com/ua/
and paste it in a notepad document. Subsequently copy your unified address and paste it at the end of the link, so that your link would look like this: https://zcashblockexplorer.com/ua/yourunifiedaddress
If you select the merged URL, and open it with your Internet browser, a Zcash block explorer will then show you your z-address and possibly your t-address.
Therefore, if you're using Y wallet and don't want people to know your t-address activity, you can use the New Snap Address feature to create a new unified address that doesn't have any data about your t-address activities.
Enjoy.