Speed date before signing
If possible, have the teams from both sides meet over a coffee or lunch. Observe how well they interact and get along with one another. Ask for feedback from your team on how comfortable they felt and would they be able to work with them. This achieves two things. One, it will save some time when the project starts as the team already have some knowledge of each other e.g. roles, responsibilities, capabilities etc. Two, your team are part of the decision to work with the chosen IT partner giving them a sense of ownership of the project.