Verizon was quick to patch the Root method and Loki Bootloader bypass on their variant of the Galaxy S4. The mod community was also quick to band together for a common goal, regaining control of the device they bought. They quickly raised a large bounty for a root method and also for a bootloader unlock. Pretty quickly a new root method was released. Credit for the exploit goes to DooMLoRD and PWM978.
Before you read any further I would like to say that I would only suggest this method for those who accidentally accepted the OTA to VRUAME7, or those who have already updated. This method will root the latest OTA update, but there is no viable way of installing a custom recovery so in my opinion you would still be up a creek. I imagine the method would come quickly with the bounty now being over $3000 maybe this will draw a developer to the project that wouldn't ordinarily work with Verizon devices. Head to the source link below for the full guide by Open1your1eyes0.