Is it a Shared Photo Stream or My Photo Stream?
If it is a shared stream and you are the owner, remove all subscribers you do not want or delete this stream. If you are not the owner, unsubscribe from the stream: See here, how to unsubscribe: iCloud: iCloud Photo Sharing FAQ
If it is My Photo Stream, then the new owner is using the same AppleID as you for the Photo Stream. Did you sell the iPhone or give it away? You should have disabled all services on the iPhone and removed it from your AppleID.
What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support
Anyway, if someone else is using your AppleID for iCloud Service, change your password immediately, Change your Apple ID password