By aligning these processes to the Agile delivery methodology, effective project management will enhance the probability of success. But you must recognize the processes are applied differently.
Some of the areas that need an Agile approach include:
Project Scope Management
Traditional project management expects scope management to define the output. The final outputs in an Agile project should be defined in terms of achieved capabilities--how the capability will be achieved will be discovered along the journey.
Change control will be more challenging, as is configuration management. The overall project needs a really good systems architect to keep each iteration or sprint focused on contributing to the big picture.
Project Time Management
In an Agile project, scheduling and workflow become closely aligned. The overall system architecture optimizes the sequence modules needed to be built in to allow progressive testing and implementation of capability.
This defines the schedule. Scheduling should be at a much higher level; each sprint is likely to be a single activity of one to two weeks' duration.
Project Cost Management
Agile projects should be based on either a cost-reimbursable system, or the client accepts scope is a variable based on achieving the maximum improvement possible for a pre-set budget. This is a totally different philosophy to traditional project governance.
Project Quality Management
This is probably easier under Agile. Quality is continually assessed by the involvement of the client and the iterative release of modules to production.
Project Communications Management
The level of trust needed to run an Agile project is much higher than a traditional project. Effective communications in all directions are essential.
Project Procurement Management
Agile works in a collaborative partnering space. In the engineering world these are called alliance contracts. Traditional contracts do not support Agile delivery methods very effectively.