According to datamined files from @FNBRLeaks, Week 5 will feature a new challenge requiring you to ‘Use a Jetpack’ in return for 5 Battle Stars:
The upcoming LTM labelled as ‘Shotguns’ in the game files contains additional information regarding a ‘Close Encounters’ Limited Time Mode described as “Close quarters combat with Shotguns & Jetpacks! If you find a jetpack, double-tap the jump button to take off. Keep the button held down to apply thrust. Make sure to land before it runs out of fuel!”
Based on this, it’s very likely that we’ll see the Jetpack added to the game either before or during Week 5 of Season 4.
Note: Files can be changed during later patches, this information isn’t necessarily confirming the release of the Jetpack or Close Encounters LTM.