If you have a project manager assigned then she/he will direct or manage the project. The first thing she/he must do is to manage the project following some project management guidelines (PMI, IPMA, GPM, or a method like PRINCE2, others). That is the first focus that is mostly forgotten.
Inside that, the project manager must use tools and techniques to work with stakeholders. Another thing mostly is forgotten mainly because when people perform project stakeholder analysis and define the strategy mostly forgot that an elicitation activity must be done to get data about stakeholders perception about impact/interest or any other thing you use in the stakeholder analysis matrix.
When all of these are in place then you can consider leadership as a variable that helps but is not definitive.