According to Respawn co-founder Vince Zampella, DLC for Titanfall is currently in development, but no release date is currently known.

Here's the tweet:

@WigNilly DLC is in the works, not quite done yet tho. Don't think we've announced a date yet.

— Vince Zampella (@VinceZampella) March 25, 2014

Zampella also confirmed that all new modes will be free. Any extra modes that are made available will not be included as DLC:

@YaBoyZD3 Modes we release will be free to all, not part of DLC.

— Vince Zampella (@VinceZampella) March 25, 2014