You have two options: (1) convert your foreign driving license to an Israeli one or (2) apply for a new one
Public transportation in Israel is well connected: you can reach most places by trains and buses. But they are rarely ever on time – sometimes, only off by a couple minutes, and sometimes, in Tel Aviv particularly, they can be off by 10-30 minutes, even on a normal evening. I missed a bus from the Red Canyon one time because the bus was 10 minutes early, and the only bus home zoomed past me as I walked to the bus station; the next bus was 2-3 hours away and I was in the middle of nowhere. That can happen. And, of course, trains and buses are shut in most parts of the country during Shabbat (Friday evening to Saturday evening) and barely operational in arguably the biggest city in Israel – Tel Aviv. Most of us are not bogged down by classes, research, or work on exactly these two days and it can be pretty difficult to get around during Shabbat.
So, there are reasons you’d want to get a driving license in Israel.
You can rent a car, buy a car or a motorcycle, like I did.

Luckily, Israel allows foreigners to drive with their foreign driving licenses for one year from the date of arrival (I suppose you’d need to carry an International driving permit, but I have never attempted to drive with my Indian driving license) . You must get an Israeli driving license, however, before you mark your first anniversary in Israel.
You have two options: (1) convert your foreign driving license to an Israeli one or (2) apply for a new one.
I can tell you how the first option works, or, rather, how it went in my case.
I had a motorcycle license from India and in Israel, I applied for “A1 license” for motorcycles.
Therefore, I recommend you research this issue further on the internet (see the useful links section) before you go about converting your license. I got my license sometime in 2021, during the COVID-19 pandemic, so some of the steps might have since changed.
Note, by the way, that option (1) is only applicable if you have had your foreign driving license for more than five years. It’s not entirely clear if you have to be in the said country for five years before you come to Israel or if the time you have been in Israel also counts. I was lucky so I never had to find this out: I had my license for just over 5 years when I moved to Israel. Also, you do not have to give up your foreign driving license.
Yalla boie (let's go, with me)
Step 1. Set up an appointment with Misrad ha’rishui, the Ministry of transport.
I recommend doing this on a browser so that you can translate the Hebrew text to English (ask a Hebrew-speaking friend to do it for you, if you can).
Go to the myVisit website and login with your Israeli phone number. Select this logo:

Eventually, it will ask you for an Israel Teudat Zehut number (“t.z.” henceforth; the Israeli social security number). If you’re a temporary resident (on a visa), like me, you will not have this number. I asked my Israeli friend for his t.z. number and entered my phone number and booked an appointment. You can use a pseudo t.z. number (a number that follows the logic all all t.z. numbers adhere to but isn’t really; my university ID is one such number) but I personally see no reason to use it unless I had no other option. Select this option:

The one in Holon was my closest center so I went there. According to this post by HUJI, there are three other such offices . If I remember correctly, the person at the counter in Holon spoke English, but if you do not speak Hebrew, I wouldn’t recommend going alone. But it will be manageable because someone will speak English and will be happy to help you. Getting this number should be relatively straightforward.
Then, you should see only option, but, in any case, select:

After that you’d just need to set your appointment and visit the Misrad ha’rishui.
Step 2. Get the number “89”.
This will be your first of the two visits to the Ministry of transport. Carry your passport and the visa. Just in case, carry your foreign driving license and any other document that might be relevant. When you reach a counter, tell them that you are not an Israeli citizen and that you would like to convert your driving license. Tell them that you do not have a t.z. number to fill up in the green form. Ask them for the so-called “89” number.
Step 3. Submit the green form online.
Next, you will need to fill up the “green” form. This form is a sort of undertaking that you are physically fit to drive. Go here: בקשה להוצאת רישיון נהיגה (govforms.gov.il) and fill up the form to the best of your knowledge. It’s in Hebrew, unfortunately, but use your browser or the power of friendship to translate.
Step 4. Visit one of the optometrist centers.
After you have filled up the green form, you will need to get (1) your photo taken and (2) eyes tested. There are optometrists who have tie-ups with the ministry of transport and will do both of these things for you. The HUJI article says that it can cost 50 shekels (I cannot recall how much I paid). I carried a printed copy of the green form with me, but I cannot recall if I needed it. I would carry it (along with the passport and visa), just in case.
Here is the directory for the authorized optometrists. I went to “Halperin” in the Dizengoff Center mall. The mall is a maze, so be prepared to be lost in it.
Step 4 (might be obsolete). Get the “entries and exits” form from Misrad Ha’Apnim[AR2]
I remember that I had to get an “entries and exits” form from the Misrad Hapnim (the ministry of population. This document notes all the times you entered/left the country. I went in the middle of the pandemic, so my document had a single line, of course.
The HUJI post no longer recommends it, so I’m not entirely sure if this step is necessary in 2023. Therefore, please check with the ministry during step 2 if this form is required.
If you happen to need it, then go to the myVisit. Enter a Israeli friend’s t.z. number and select Misrad Hapnim:

I went to the one in Ramat Gan:

I see that website does not have an option for the “entries and exits” form, so I’m not quite sure how to go about it. But in my experience with the Israeli bureaucracy, you can select any option and just get into the building. Once there, inform the official of your situation and they’d be able to help you out.
Step 5. Another visit to the Ministry
At this point, you have everything you need to get your Israeli driving license. Go back to the myVisit website. This time though, enter your new 89 number to get into the system (if it doesn’t, “phone a friend”) ;)
Carry your passport, visa, and your original foreign driving license (and any related documents you can think of, or you were given at any stage of this process). When you’re at the counter, tell them that you would like to convert your foreign driving license to an Israeli one. Submit your documents and you should receive a temporary “paper license”. It will be valid until you receive the proper “plastic license” via mail at your home address. My plastic license mine is valid for three years and expires soon.
You’ll need to pay around 220 shekels for the plastic license. You will receive a payment voucher at the ministry: take it to the nearest post office and you can pay there.
Useful links
HUJI: file_drivers_license_conversion_-_guide.pdf (huji.ac.il)
Converting your Foreign Driver's License - Nefesh B'Nefesh (nbn.org.il)