Staggered wheel setup- understeer?

Right now I have 15x7 all around.

I'm getting some new wheels, thinking about 15x7 up front and 15x8 in the back. Will this cause understeer?

That is an oversimplified question. It is impossible to properly answer based on several bits of missing information.
Look at what leads to understeer and oversteer as one guide, Also take consideration that the automakers built the cars with a strong bias toward safety and control. UNDERsteer is naturally self healing. One understeers, then slows down until control comes back to them.
One rule that seems to hold true: The end of the car with the greatest roll stiffness will lose traction first.
Stiff leaf springs and a fat rear sway bar on a car with stock torsion bars and no sway bar would very likely result in oversteer when subjected to quick maneuvers.
All high performance sports cars have different wheel and tire sizes front/rear. Of course, any disparity between the grip is offset by chassis engineering.
I run a 295 rear tire and a 275 front. Mine is neutral until I stab the throttle to kick the ass end out.

Missing a heck of a lot more than several bits of information.

"I'm getting some new wheels, thinking about 15x7 up front and 15x8 in the back. Will this cause understeer?"

With only that little of info, the most accurate simplistic answer would likely be, it will change the balance, whatever that currently is, and it will be TOWARDS understeer, which maybe is your objective?

so no tire size change? a 1" wider rim at the rear will not do much at all. an air pressure adjustment would be a bigger ....

This book, one of the best car books I have ever read of dozens, has one line of many, that hits the nail on the head best regarding car modifications:
" Everything effects everything else"

Think-fast-the-racers-why-to-guide-to-winning_by Neil Roberts