Timelines:

#3, the Present, Clint and Nat (they know the 10Rs are still active) learn about a new plot; something involving Tony now that he's out. They decide to head it off. Also Red Room.

#2, the assignment in the past = Red Room stuff.

#1, Clint's assignment to assassinate Nat. She's working with Ivan Petrovich (AKA Anton Vanko, the man who worked with Howard in the 50s). Ivan/Vanko gets away, and Nat defects to SHIELD.