You need to update to internally managed kernel. Go to Control Panel, select your Droplet, click Kernel. From drop down select GrubLoader v0.2 and change kernel to it. When it does finish power off your Droplet and power on again (power off is required, restart will not change to new kernel).

With this, you can manage kernels from Droplet. If you execute:

sudo apt-get update && sudo apt-get dist-upgrade

This command will update your Kernel to latest available - 4.8.x.
For specific kernel you’ll need to specify which one you want.

All I wrote above is available in How To Update Kernel. Especially pay attention to changing to GrubLoader and to Installing an Arbitrary Kernel on a Droplet if you want specific version.