What are team requisites?
Complete several requisites of the same team to unlock new contract types with the team. In total, there are four contract types: Rookie, Challenger, Expert and Master.
If you complete one requisite, you will unlock a Rookie contract. However, if you complete two requisites for the same team, you will then gain access to a Challenger contract with this team. If you complete three requisites of a team, you will be able to sign an Expert contract and if you complete all of the team's requisites, you can sign a Master contract.
Some teams only offer one, two or three different contract types. For instance, to sign a contract for Mercedes, you have no choice but to complete all of the four requisites of the Mercedes team. You cannot sign a Rookie, Challenger or Expert contract to drive for Mercedes in Career mode.
If you sign a Challenger contract, you will only be able to sign Challenger or Expert contracts as all the teams will stop considering you as a Rookie. Same goes for Expert and Master contracts, if you sign a Master contract, you will only be able to sign Master contracts with each of the ten F1 teams. However, keep in mind that you will still have to complete the Master requisites before signing a team's Master contract.
What are team missions?
After signing a contract, you unlock new team missions to complete during the season(s). Complete the team's missions to obtain R&D boxes containing chassis parts of the Team's F1 car to upgrade its potential in Career mode and also in other modes.
Rest assured that if you didn't complete all the team's missions after finishing a season, then, you will still be able to complete these missions next time you sign a contract with the team.
Each contract type (Rookie, Challenger, Expert or Master) features new exclusive missions. Still, if you haven't finished all the Rookie missions of a team, when you will sign a Challenger contract with the same team, you will inherit from the Rookie missions that you didn't complete along with the new Challenger missions.