It is very likely that if you don't manage to obtain tax the vehicle (strictly now called VED) that you will be pulled over by the police, who are enforcing the law apropos non-essential travel. I take it that the car has a current MOT and that your wife has taken out insurance for the vehicle (if she is using it for work to drive to and from clients homes, she will need business insurance). Whilst using or keeping a vehicle on the road without it being tax is illegal, she may find that the police are lenient. They are likely to do a moving vehicle check on any vehicles they stop.