According to statements of the company is not currently planning the release of Spotify native app for Apple TV.

The support TVOS is not considered primary according to the words of Samuel Erdtman in a discussion about GitHub: You should not expect a release for TVOS in the near future. I’m sorry.

Users who have another Apple device can use AirPlay to play audio streaming on Apple TV, but a native app would exploit user interface aimed at for your TV.

The Apple TV media lack naturally represents a slight advantage for other music streaming services like Pandora and the same Apple Music Apple.

Source: AppleInsider