At the end of "Agents of S.H.I.E.L.D." season two, we saw the agents battle the Inhumans that eventually led to the events in "Avengers: Age of Ultron" as well as Jemma Simmons (Elizabeth Henstridge) being swallowed by Symbiote-like substance.
If you may recall, this substance was similar to the one that engulfed Graviton in season one. The mystery behind its origin and existence may lead to speculate whether Symbiote is the same one that gave Peter Parker aka Spider-Man the mighty power of Venom. However, there are odds against introduction of Symbiote before at least Spider-Man is introduced in "Captain America: Civil War".
We already know that Project Centipede is backed by Hydra that infiltrated S.H.I.E.L.D. There is a strong possibility Hydra will have a more active role in season three. Baron Strucker (Thomas Kretschmann), leader of Hydra, was killed by Ultron (James Spader) in "Avengers: Age of Ultron".
However, in the last episode of season two, agent Grant Ward (Brett Dalton), seeking revenge on S.H.I.E.L.D, found some troubled men and took them under his wing. These men may constitute to form the new Hydra. Apart from it, A.I.M. and perhaps MODOK may be introduced.
The characters of Barbara "Bobbi" Morse aka Mockingbird (Adrianne Palicki) and Lance Hunter (Nick Blood) were introduced in season two and were well received by the audience. Similarly, season three is likely to introduce more prominent characters from the Marvel Universe.
Emily VanCamp, who played Agent Sharon Carter in "Captain America: The Winter Soldier", may reprise her role in season three prior to release of "Captain America: Civil War". To gear up for Civil War, she needs to be fully adapted and introducing her will be a good move.
Lady Sif of Asgard (Jaimie Alexander) made an appearance in both season one and two. So there is a possibility she will show up in one of the episodes in season three too.
Apart from it, at a press conference in 2015 Comic-Con International, San Diego, "Agent Carter" show-runners Tara Butters and Michelle Fazakas said that "there's a thing called Darkforce that comes from the comic book universe, which also created Blackout on Agents of S.H.I.E.L.D. and it comes out of the Doctor Strange universe as well.
That is going to show up in next season of Agent Carter, causing problems for people." Given that Darkforce was already shown in season one of Agents of S.H.I.E.L.D. where Marcus Daniels aka Blackout (Patrick Brennan) was able to tap into its powers, we can expect a cameo by Doctor Strange too.
Other members of new Avengers like Ant-Man and Black Panther may also make a cameo.
Possible Tie-in With "Captain America: Civil War"
It is likely to see season three plot elements leading into Captain America: Civil War as season one led to "Captain America: The Winter Soldier" and season two to "Avengers: Age of Ultron". Like the last two tie-ins, season three may also build up on a story line that will eventually form the plot of Civil War.