The steering on my '07 TL-S has some noticable free play when in the center which wasn't there before. Also, it tends to pull left or right during rough/bumpy roads.

Can it be an alignment/balance issue or something else?

I currently have the 32 PSI on all four tires and the tires are brand new about 8k on them. The car has 36k miles. TIA.

 

Have somebody check your tie rods and get an alignment done for sure. Every place should do a free suspension check with an alignment anyway so I would say start there Goodluck