Sony has announced that PlayStation Plus Premium will not support DLC and add-on content when streaming a title.
What this means is that if you have DLC for a PS3 game, you won’t be able to play the additional content, and the only way to play PS3 games is through streaming.
Also, if you plan on streaming through your PC, there are minimum requirements to stream games through the PlayStation Plus Premium.
Launching June 13 in the Americas and June 22 in Europe, PS Plus Premium will include all the benefits you currently get with PlayStation Plus, as well as a library of 400 PS4 and PS5 games, classic games from PS1, PS2 and PSP, time-limited game trials, and PS3/PS4 game streaming.