Add a field from second record (of the same person) to a report?

Do you just need to identify the most recent Team? The simplest way would be using the relationship to find the 'most recent assignment' Record ID# that isn't current and create a reverse relationship to that assignment based on that value to bring in the old team. What that looks like in practice is: 

In the current summary between Staff and Assignments - make a summary field of the Max Record ID# where the status is Inactive. This will get you the most recent assignment RID. 

Create a new relationship where Assignment has many Staff (the reverse of your current) and when it asks you to define the related field, pick the Max RID from above. This way your relationship connects automatically to the most recent assignment. 

With the relationship, add the Team Name as a lookup field and rename it to 'Prior Team' or whatever you want. 

You could also do the above without the reverse relationship if you prefer not to. You could combine a handful of summary lookups in your current main relationship to find the Max RID, bring it back down and then do a combine-text summary field where RID = the Max RId, or you can go the formula query route. Lots of options to achieve the same goal.