Vacuuming is the best bet, do all the carpets with a good upright BUT! do NOT overlook the fact that allergies to 'cat hair' are actually allergies to the dander. So, whilst you will of course want to remove as much hair as possible, the dander -which will be on all surfaces and walls- will need washing away too.
Were it me i would be very wary about making any promises about the quality of the clean you do in case the new tennants still have problems. I myself have allergies to cats and it's made far worse by the fact that i spend my life avoiding them. Because of this i really do suffer if i spend time in 'catty' places. I can't help but wonder if the new tennant (who i assume avoids cats like the plauge) will still struggle, even after cleaning?