Entity Reference - Auto complete field in content type
You can do this in various ways.

An easy option would be to display a view as the field. There are quite a few solutions that enable you to do so, such as:

Viewfield,


  Viewfield provides a field that holds a reference to a View and
  renders it whenever the entity containing the field is displayed.


Field Embed Views, 


  The module provides a field type to attach any Views View display
  with, configurable on per-entity level, default values for exposed
  filters and sorting.


EVA,


  "Eva" is short for "Entity Views Attachment;" it provides a Views
  display plugin that allows the output of a View to be attached to the
  content of any Drupal entity.


Panels, Display Suite,  etc.

The view will list partners and the contextual filter will be the current project you are looking at.

If your field is also an entity reference field, then you should probably look at Corresponding Entity References.

Think about your solution where you will be duplicating database storage (both ends of a relationship) when one end can easily be computed (via an sql query for instance). Maintaining the data on both ends means more work as you have to synchronize it constantly, as well as more storage. Maintaining the data on one end only and making the other end purely a display issue is more maintainable.