A Verizon model of the Gear S3 Classic has shown up at the FCC recently labeled as the SM-R775V. This follows the Frontier version of the Gear S3 for Verizon which passed through the FCC last month around February 14th carrying a similar model number, which was listed as the SM-R765V. The "V" in this case would be denoting that the device is meant for the Verizon Wireless network as all Verizon devices tend to have a V on the end of their model numbers, so even though the FCC documents do not explicitly mention that this is the Gear S3 Classic for Verizon, the V is suggesting as much.
What's intriguing about Verizon getting its own model of the Gear S3 Classic is that the regular Gear S3 Classic that can be purchased through Samsung or other retailers is capable of connecting up to Bluetooth and Wi-Fi only for accessing any of the features that require data. According to the FCC documents for this model of the Classic, though, it will apparently have connectivity options for LTE in addition to the Bluetooth and WLAN options, which means that Verizon seems to be getting an LTE variant of the Classic that can connect to the internet through the use of a SIM card just like all of the Frontier models.
If this is the case then it may also mean that other carriers will get an LTE variant of the Gear S3 Classic as well, though so far there is no indication of this. With this model of the Gear S3 Classic passing through the FCC it's possible that Verizon could be preparing to launch it on store shelves and on their website in the near future. Whether or not the cost would be the same as the standard Gear S3 Classic or end up costing more is unclear, so it's still possible that both the Gear S3 Classic and Frontier models on Verizon could cost the same amount since they'll both be able to connect up to the Verizon cellular network. It's also unclear as to whether or not Samsung had planned all along to launch an LTE version of the Gear S3 Classic, as it wasn't mentioned in their announcement for the watch last year that an LTE model was going to be produced.