You can drive in Kuwait under an International Driving License if you have arrived on a Visit/Business Visa but NOT an NOC. The International License must be insured and only lasts the length of your Visa, normally 1 month.
If you have entered Kuwait under an NOC, you can apply for a temporary Driving License until your Residency procedures are completed AND you have your Civil I.D. after which, a Full License can be obtained, this takes about 2 months. So you should apply for a 2- month temporary Driving License.
The procedure is, normally, as follows:
Obtain a translation of your Driving License. Take a photocopy of your License. Your Embassy can do this for you.
The translation must be attested. Your Embassy will do this as well. Now the cost of this should be 15KD. But some people got it done cheaper for 12.5KD!
Do all this at the Embassy, and at the same time, you can register at the Embassy as a citizen of your respective country, residing in Kuwait (eg - U.K. citizen residing in Kuwait).
Next go to the Ministry of Foreign Affairs ( located in Cairo Street ) and get your translation "attested" AGAIN! Cost 4KD. An Arabic speaking " Minder " is recommended, to help you through the System.
Now the next step is to obtain an Application form from a Police Traffic Department. Here is where you could run into difficulty since you are supposed to go to the Traffic Department in the area in which you live. ( For Salwa, it is Jabriya ).
However, many people have managed to get sorted out at Shuwaikh Traffic Department. It really depends upon the Official who deals with your Application.
Get the "Minder" to fill in the Application form in ARABIC, English will NOT do!
Report to the Senior Officer and he will ask you to see the Director of the Traffic Department who, hopefully, will sign to say you do not need to take a Kuwaiti Driving Test.
The remaining steps are really in the hands of your "Minder" and luck. But all the process is possible at Shuwaikh. You end up with a 2 -month Driving License.
The permanent License is only obtainable when you have got your Residency and Civil I.D., an eyesight test (in addition to the one you will need for your Residency) and a Blood Group Certificate. Again use your "Minder" to get through the System.