Assuming this is the first sector, I 'think' you have to rebook into the original booking class on the new flight (and pay any fare difference) and then u/g into the fare bucket you want - I for u/g to Biz. I had to do it this week and, even though I had already upgraded to Biz on my original flight, I had to re-book into Y on the new flight and then re-upgrade.
It seems a lot easier to do it at an Emirates booking counter than over the phone.