Yes it can possess energy.
First let us recall types of energies, there are different type of energy exists, some of them are thermal, kinetic, potential, chemical, gravitational, electrical, radiant, etc.
So if any object suspended in space without gravity, it can have kinetic energy (due to motion).
If object is not also moving then also it can have thermal energy, chemical energy or radiant energy.
Since most of the time we deal with kinetic and potential, It must be clear in our mind that energy is not only kinetic and potential.
I hope its clear.