The pix would indicate that whoever installed the brick veneer front didn't bother to tie same into the wall's framing members underneath (using brick ties), nor did they bother trying to bond the new brick into the existing at the corners by removing alternate half-bricks and replacing with full bricks projecting a bonding pattern into the front wall's brick lines.
Doing the latter can still be done by an experienced mason, but it could prove to be a bit expensive. And there's still no guarantee that the front wall won't continue to want to move, without the ties to hold it in place. Maybe a ledger bolt system, with counter-bored holes in existing bricks for the bolts to pass through, lagged into the wall's studs, and then be mortared over? (I dunno, I'm not a mason).