No. A travel eSIM is a separate, additional SIM profile on your device. Your existing SIM remains untouched and active. Modern smartphones (iPhone XS and newer, Samsung Galaxy S20 and newer, Pixel 4 and newer) support multiple active SIM profiles. The travel eSIM is installed alongside your original SIM rather than replacing it. You choose which line handles which type of traffic in your phone's settings.
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Installing a travel eSIM is a software operation that adds a new SIM profile to your device's secure eSIM storage. It does not modify the physical SIM card (if you have one) and does not modify the eSIM profile your home carrier has installed.
After installation, your phone shows two (or more) SIM profiles in the cellular settings menu, each with its own carrier name and signal indicator. The phone can hold multiple eSIMs simultaneously (limits vary by device — newer iPhones support 8+ eSIMs stored, with 2 active at any time).
When you no longer need the travel eSIM (returning home), you can either disable it (the profile stays on the device for future trips) or delete it. Either action affects only the travel profile; your home SIM is unchanged throughout.
The "does this affect my normal SIM" answer is universal across providers. Whether you buy from QuiqSim, Airalo, Holafly, Saily, or any other travel eSIM service, the home SIM remains active and unmodified.