....and here are the team ups that focused on those characters!
Old Agent New Name
A bit of a spoiler here, but that agent was Bobbi Morse (who had been working for S.H.I.E.L.D. with Ka-Zar back in the days Ka-Zar appeared in Astonishing Tales), then as the Huntress in Marvel Super Action #1 of 1976 (which featured a lead story on the Punisher). There, as here, Bobbi had been working to find spies with S.H.I.E.L.D., with Peter Parker returning to New York from the West Coast, and seeing a beautiful blond in a trenchcoat being chased, and he changes into Spider-Man to help out (along the way, seeing her get shot, but surviving due to her insulated costume, and fleeing from their flying car!). Mockingbird introduces herself to Spidey, and informs him they were battling S.H.I.E.L.D. agents, which upsets Spider-Man, and Bobbi takes off away from him, leaving Spider-Man to deal with S.H.I.E.L.D.'s Manhattan director, Carl Delandan.
Ex-Agent All Hero
former agent of S.H.I.E.L.D., who left the agency to work for Project: PEGASUS, the mighty Quasar, who teamed with Spidey in Marvel Team-Up #113 (January, 1982) in "The Resurrection Of Edward Lansky" by writer Mark Gruenwald, penciller Herb Trimpe and inker Mike Esposito (with a cover by John Romita, Jr. and Frank Giacoia).
While on his way to class, Spider-Man encounters a Project: PEGASUS vehicle taking the dangerous villain, Nitro (whom Spidey had recently defeated), to its headquarters (with Quasar heading the team), and Spidey and Quasar get into a discussion, with Quasar later heading to go Empire State University.
This leads to a battle of Quasar and Spider-Man, but Quasar regains control of himself, and then the two heroes work together, restoring Lightmaster to his own body (that of Edward Lansky), yet still taking him captive (for the crimes he had committed). Spidey and Quasar don't part happily, which is odd, as Quasar usually gets along with everyone, soon after getting his own series (written by Mark Gruenwald, who also revived Mockingbird in the Hawkeye mini-series) and Quasar becoming an Avenger!
The Boss Is Back
Before Colonel Nick Fury was the head of S.H.I.E.L.D., he was just a sergeant in World War II, leading a team of combatants there, called the Howling Commandos. One of that team's members was called Dino Minnelli, and the crime family of the Maggia kidnapped his girlfriend, actress Julie Winston, getting Nick Fury and Spider-Man involved in the case.
Even worse, the Maggia has some help, with an old weapon Hydra created to attack S.H.I.E.L.D., the robot Dreadnaught! Sadly for Dino, it seems her acting included their relationship, as it was all a plot of the Maggia, who is heartbroken after this event.
Captain America, the Falcon, Iron Man, the Scarlet Witch and the Black Widow! It seems Spider-Man and S.H.I.E.L.D. hold the Marvel Universe together!