This chapter of the guide to Dragon Ball Z: Kakarot has a walkthrough for The Mystery of the Missing Tail side quest.
Time frame: From Evil Emperor Frieza - Episode 8: Intermission - Episode 8: Intermission
Reward: 45,512 EXP, D Medal, Celebrity Fan Photo
Where to start: South-Eastern Islands, as Gohan.
Let's start with the fact that you can't have Vegeta in your party if you want to begin this mission.
Talk with Oolong and then fly to Kami's Lookout Area.
There, talk to Kami - he is waiting for you in front of the building.
After that, head to the Central Plains Area. You must fight Vegeta. After winning, go back to Oolong to complete the mission.