Cyclic carbocation rearrangement
1,3- and 1,4- shifts don't really happen. It's just too far away. If you have a double bond at 4 or 5 carbons away, maybe you can do a ring closure or form a non-classical carbocation. The cation you've drawn could however undergo a sequence hydride shifts. Each hydride shift would move the cation closer to the methyl group, until the 3rd shift places the cation on the tertiary carbon. You'd need to out-compete any kind of elimination or cation reaction with a nucleophile...