So, having watched the series Agent Carter, this show is taking place 1 year after the events of the Captain America. Now, if you watched the Marvel One Shot of the same title, those events also take place 1 year later. Yet, at the end, they mention SHIELD and the fact that Carter/Howard are going to be running it. So, chronologically, whats going on here? Did they dismiss the One Shot?
According to the series creators:
The show would start in 1946, sort of in the middle of the timeline of the One Shot. McFeely said, “We can’t get her to the end of S.H.I.E.L.D. that fast. We wanna stay in that world longer where people are disrespecting her and she’s proving herself and going on missions and things like that.” (source)
There is one bit of discontinuity with that timeline, however. In the one-shot, Carter works for an agent named John Flynn, head of the S.S.R. However, for the entire duration of Season One, Carter works for S.S.R. Chief Roger Dooley, and no mention is made of Flynn.
Without inventing some excuse for why Flynn never appears on-screen, it seems difficult to reconcile the two as happening simultaneously.
It would have made more sense, however, if the short took place immediately after the TV series Season 1, for several reasons.
First, during the one-shot, Flynn refuses to send Carter into the field, but does utilize her for her codebreaking skills. However, in one of the later episodes in Season One, the SSR brings in an outside crypt-analyst to break a Russian code, and Chief Dooley seems taken aback when Carter is able to crack it herself. That implies that she has not (yet) spent any significant time as a code breaker for the SSR.
Dooley dies in the season finale, leaving an opening for Flynn to come in and take over.
And finally, as Season 1 wraps up,
Peggy is unsure if she's going to remain at the SSR, putting her in the perfect position to be recruited by Stark for SHIELD.
The show takes place first, followed closely by the short.
IGN asked showrunner Michele Fazekas about this:
IGN: How will that work with the short, because I think I’ve heard it kind of takes place in between? Does the short still exist, or are you going to be telling a new version of that?
Fazekas: If you think of the short as sort of the end of the series, the series would be leading up to that moment where she gets assigned to SHIELD. (Source)
This is consistent with the details of the show and the short. In many ways, the events of the show appear an impetus to Stark Sr. to evaluate the SSR's shortcomings and start thinking about replacing it.
The "One Year Later" and "1946" tags in the short and show, respectively, are not such a huge problem. Less than a month elapses in the show - the short could easily follow the show without pushing it into 1947.
All this may change if Marvel decides they want another season of Agent Carter, and they want it to take place before SHIELD is founded. They will be very careful about retconning an expensive short, though, so that's unlikely.
Although it doesn't always tell you the evidence for its claims, this timeline is an awesome resource for the chronology of the MCU.
I think the most likely answer is that it was set after Captain America : The First Avenger and before the two seasons of Agent Carter. Due to a file in the one shot showing the date and the first episode of the second season displaying on the screen that it is set in 1947, it makes more sense than it being between the two seasons. Howard probably launched the idea of S.H.I.E.L.D to her after the one-shot, as we saw begin to happen at the end of it. However, he then was a suspected traitor, so the project was not launched and by the time his name was cleared, Peggy was busy with the SSR.
Imagine it this way. After season 2, Carter gets reassigned to New York... With the untimely death of Jack, they needed good agents. She returns to agent Flynn, who is now in charge after the untimely death of Jack. She re-enters back into the sexist world of male agents, who have heard about her but are threatened by her... she and her talent again are suppressed, so she goes again on a mission to prove herself... Flynn is moments from punishing her, and just then Howard calls and rescues her.
Thus, season 1-2 happens immediately after Captain America, the one shot happens immediately after season 2.
The One Shot Agent Carter Starts off on exactly 3/15/46. She gives a fellow agent a file of analysis on recent transmissions dated 3/14/46 . She completes a mission and Howard Stark is about to kick off shield with Peggy running it.Howard loved Peggy so Flynn being a jerk to Peggy and Howard being Flynn's boss at that time explains Flynn's Sudden absence. Fired.Mar 46 is one year from Steve Rogers going missing in Mar45. A month later Howard becomes wanted for treason. No more shield talk for now because Howard might be a traitor.The Zodiac she retrieved on the her mission becomes a focal point in an episode of agents of shield over 70 years later. The very first episode of the TV series show her flashing back to the month before, the night of the Zodiac mission 3/15/46 It's should be placed behind Captain America the First Avenger and ahead of both seasons of the TV show