To do this navigate to:
  1. Core > Security > Roles. 
  2. Click Add.
  3. Title the new Role and mark off the Radio Button next to Platform Manager. 
  4. Click Next to move to Step 2.
  5. Click Next to move to Step 3 (the tasks to edit the Contact Card are embedded into the Platform Manager Role).
This will give the editing capability on the Contact Card only and will not give access to Core or any other tasks.