Sounds like you both have the standard non-bose system in the A3 which uses a separate amp in the sub enclosure to power the rear speakers, and IIRC the sub, while powering the fronts off the head-unit's amp. If you change the head unit, then the feed to this external amp is no more, so you have 2 basic options:
1. Run new cables from the rear speakers back to the rear amplified outputs on the new head unit
2. Buy a cabling adaptor that goes behind the head unit to send the signals back to the Audi amp in the sub enclosure in the boot, although the standard amp is low powered compared to the head unit's built-in amp, so you are better off with option 1.
There are other more exotic options, like a new amp and an AndyMac stealth sub, but all that requires some more new cabling, and costs money naturally. Depends what you are after and what you are prepared to spend.
A search on the forums for 'a3 rear speakers' brings up plenty of discussion on this sort of problem.
Cheers,