Is it possible to recover current texts after restoring from an old backup? I restored my iphone 4s from a 1/2/2013 backup. Looks like I lost everything that was current like texts. Can I get it back to the state it was in before I restored it from that 2013 backup?
Only if you have a more recent backup.

Do you have iCloud Backup set up on the phone? If so, you most likely have a more recent backup on iCloud.