If my car get hit by an insured driver can i claim a hire car of his insurance?

UK? Yes you can. If the third party admits liability or is found to be liable they are responsible for your costs. This can include the cost of you hiring a car whilst yours is off the road. You can claim against them for any cost you would not have incurred had the accident not happened, so this could include say contents of your vehicle, time off work due to your injuries, replacing clothing etc.

Back to answering your question specifically, they are only liable for the hire car costs to the point where they settle your claim in full. So if your £1000 car is a 'total loss' they are liable for your hire car costs whilst making their mind up whether to repair it or not. Once they have decided and paid your £1000 it is up to you to buy a new car. Thus they do not have to hire you a replacement indefinately.