Power struggles, increased pressure and ticking clocks, relationship friction, duty and responsibility, loss of control

This conflict is most likely to happen in your character's job, but it might also come about if the character is in school, a club, organization, sport, there's a group activity, or other situations like an arranged marriage or social pairing. Think outside the box to come up with an unusual partner combo. 

Being saddled with the boss' entitled and clueless kid as an intern
Getting stuck with new recruit (as a police officer or similar job)
Being told by parents to buddy up with the new kid next door
Having to work on a school project with someone who is unmotivated
Having a slob for a desk mate at work
Partnering up with someone with a poor work ethic
Being assigned to a "poor performer" to try and turn them around
Being matched with a dance partner, fellow actor, or co-host that the character can't stand
Having to work with someone who is not a good personality match
An arranged marriage proposal that disappoints

Power struggles 
Personality clashes
Arguments 
Uncomfortable silences
Competition and trust issues getting in the way of teamwork