Recently, our company signed a contract with a very important customer. I am assigned to be the leader of a new team, and therefore am requested to travel frequently. Much over-time work is also inevitable.
"Good contract" doesn't work well. It'd replace 'good' with another adjective like 'important', or just not include it at all. It's assumed it's good if it was with a very important customer.
"New leader of a new team..." - Not wrong, but the first 'new' is redundant.
"...have business travel" - I don't know exactly how you mean to phrase it... 'business travel' is a noun. You can just say 'travel' as a verb and 'business' is implied from the rest of the sentence. You can say "...travel on business frequently" if you wish.
"...much over-time work is also inevitable." Doesn't really fit the structure of the rest of the sentence. You can say it, but it's awkward. I suggest you start a new sentence.