3.10 is too old, how can tk1 upgrade the kernel to 4. or above 3.19
There is no official support for that. The most you will see as an update for the TK1 is possibly a security fix. The software development reached end of life several years ago, and includes all 32-bit platforms.
I am not saying a newer kernel could not be built, but it would be an extreme effort even for someone who works on kernels. Perhaps it sounds a bit lame, but if you really want to use the GPU, then perhaps you should consider the 64-bit Nano. This is a significant boost over the 32-bit TK1 in both performance and using less power to get that performance (plus 64-bit is being developed).
The 64-bit platforms are using the 4.9 kernel.