I think the title speaks for itself. I'm curtently designing an alien civilization that is billions of years more advanced than us. Now this species has left behind its primitive insticts of greed and desire for power. Therefore their species is completely peacefull. In addition to be more advanced, everyone on their planet has a vast understanding of the universe (think of it like the main character from the movie "Lucy", that's how smart they are). Now my quiestion is, would such a species have the need to entertain itself.
Depends what you're calling "entertainment." Human societies produce art, music, dance, and storytelling (which can be written if the technology exists in the culture). The more "advanced" a society is, the more people can be freed to do these things part-time or full-time. If there's no greed and there is peace, etc, then artists would be valued members of society and encouraged to make art. Meaning there is no need to "go get a job." If there is money (as a concept in the society) then they're paid for their artistic work. If there isn't money, then their basic needs are taken care of.
You see this in many places, not just modern ones. For example, Jewish communities have for centuries supported men (and their families) who wanted to study full-time. Some could make money teaching youth but not enough to "make a living" for most. If the activity is valued and the society is such that it can spare some workers, then it happens.
I'd consider studying for the joy of it to be entertainment, as well as countless other things. Perhaps you mean performances? Entertainment for observers not participants? Even so, I can't imagine a society without it, even one in crisis would have songs and stories. (Think of the songs, dance, music and more than came from American slaves, for example.) It keeps culture alive.
It might be necessary for the children of an intelligent species to play. Many games require the player to imagine herself or himself in a different situation ("I'm the cop, you are the robber. Bang!"), others require the player to manipulate tokens according to rules ("You rolled a three. Move three fields forward.") Either one prepares the child for challenges in adult life. Other entertainment like reading/watching fiction may work the same way.
And if children must play, it is entirely reasonable that adults of the species retain both the capacity and the desire to play.