Proper way to follow up on interview process

Hi guys - just wanted people's experiences or thoughts on following up properly in a lateral recruitment process.

I've had interviews with 4 people in the team. 3/4 of the interviews went very well. Great cultural fit and I could talk through my experience well. There was one person who was very senior and I found it hard to connect and I think it may have hurt my chances given they haven't reached out since my last interview a week ago. 

In the past I have simply emailed my interviewers and they would help me chase up the team but in the current process I am in I am considering calling the VP who reached out to interview me because I felt we bonded and I calling would be more personable and further demonstrate my interest in the role. Obviously, the counter argument is I would appear desperate and have no other options.