While tha amount of time dilation isn't as extreme as something going at .9 c, it is still enough to make some significant difference between the planet and objects in the rest of the galaxy.
Since time is money, this could be exploited for various economic effects. The simple example of a person collecting compound interest in the outside galaxy while residing on the planet shows some of what is possible, and eventually many more subtle and complex financial instruments could be devised based on the time differential between the planet and the remainder of the galaxy.
The other effect which comes to mind is the use of the planet for long term storage. Items which have limited lifespans but command a high value could be stored on the planet and have their lifespans artificially extended due to the time dilation effect. Of course, don't expect this to allow you to store a bottle of wine for millennia, the time dilation effect is not all that great at .6 c
Realistically, if there is a desire to use time dilation for political, economic, social or military ends, it would make more sense to either build some sort of construct near the event horizon of a black hole or travel at relativistic speeds in order to take advantage of the Lorentz factor.