You can only sign a new sponsor deal when your current deal expires.
 
If your sponsor deal has expired you will see a button on your club page saying "Sign Sponsor Deal". Click it to sign a new sponsor deal.
 
If you have a sponsor deal already that has not expired, you can find it by:
1) Go to your club page
2) Click the finance button on the lower right corner
3) You will land on your finance sheet. Swipe one time to see your current sponsor deals status.