Question to folks who respond and experienced managers: how do you deal with peer managers who're not as supportive and out to get you?

Context: I joined a startup and I'm leading a new function for this org. While I have decent relationship with all others, one of my peers is far less supportive, demonstrates his value/("we made this call before you joined") at every opportunity, and even wanted to push through some of the tasks/projects on me/my team where we need not be owner but partners.

Management is supportive of me as well but said peer has a stronger rapport and I don't want to be finicky about this to the management.

How do you rightfully pushback in this scenario then?