I bought iShredder Android to securely erase my old phone. Can I continue using the app on my new phone afterward, or do I have to buy it again?

Yes, that is usually possible without any problem. If you purchased iShredder Android through Google Play, the purchase is tied to your Google account. Sign in on the new device with the same Google account and install the app again. According to the current Protectstar FAQ, an app purchased through Google Play can be used on up to three devices at the same time.

If the unlock is not recognized immediately on the new device, restart the device once and restore the purchase if necessary. If you purchased directly from the Protectstar Online Shop, reuse instead works via your activation data. So you do not need to buy iShredder again just because you securely erased your old device first.