I have recently convert my Malaysia driving license to Singapore driving license during Covid-19 period.For expat or permanent residents who posseses a driving license from your home country like myself here, you can do you conversion based on the following steps below. But do take note that any foreigners who are above 18 years old and hold a valid work/dependant/student pass are allowed to drive in Singapore with a foreign license less than a year. But all Singaporeans and Singapore Permanent Residents musth have a valid Singapore driving license to be eligible to drive in Singapore.

Here are my steps on how to convert my foreign driving license recently:
NOTE: This is only applicable if you got your foreign driving license before you obtained your Singapore Permanent Resident status.
Step 1:
Pass your Singapore Basic Theory Test (BTT)
You need to register at one of the 3 driving centres in Singapore for the basic theory test:
Singapore Safety Driving Centre
Address: 2 Woodlands Industrial Park E4, Singapore 757387
Telephone: 6482 6060
Bukit Batok Driving Centre
Address: 815 Bukit Batok West Ave 5, Singapore 659085
Telephone: 1800 666 8888
ComfortDelGro Driving Centre
Address: 205 Ubi Ave 4, Singapore 408805
Telephone: 6841 8900 / 6848 0617
Due to current Covid-19 situation, you will need to visit the respective website to make an appointment to go down to book for the Basic Theory Test (BTT). Once the appointment is fixed, head down to the driving centre on the scheduled date to book a date for your test. The administrative fee charge is S$5 and the test is S$6.50. They will issue the receipt and included the appointment date on it as well. Keep it well as you need to bring along on the test date.
You can get the Basic Theory Book from Popular Stores retailing at S$6.00 or the Question Book at S$8.00
P/S: The theory test result is lifetime and there is no expiry date. I passed my test in 2015 and I just converted my license in 2020. The driving centers and traffic police system will have it registered in when you provide them with your NRIC to check the status.
Step 2:
Attain the Abstract from Jabatan Pengangkutan Jalan Malaysia (JPJ)Once you passed your theory test, you need to obtain the letter from JPJ.Here is the sample of the letter issued by JPJ and this letter only valid for 6 mths from the date of issue. Thus, make sure you get your conversion done within the period.
For JPJ in Johor Bahru, head down to the office located at Taman Daya and it is said that the letter costs RM10.00 ~S$3.33 and payable at the counter. Please make sure you keep the receipt because it is required during the later stage.
Due to the pandemic and I am unable to go back Malaysia to obtain the letter, I approached a runner to assist me on this. All I need to do is to provide him my scanned copy of Malaysia IC & Driving License and he will settle for me. And during this tough period, it took quite a while for him to obtain the letter and I made arrangement to courier the original copy to Singapore. The cost for the runner to obtain the letter is RM60.00 ~S$20.00.
Step 3:
Apply for Conversion at Traffic Police Department
Once I got the letter or they called it Abstract from JPJ, you need to prepare the following documents before heading to Traffic Police Department located at Ubi Ave 3.
Here are the documents required to bring along for conversion:
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Original and a photocopy of your passport and NRIC/Entry & Re-Entry Permit/Employment Pass/Dependant Pass/Social Visit Pass/Work Permit
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Original and a photocopy of your valid Qualified Foreign Driving Licence
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Processing fee of S$50.00 (Cashcard and NETS payment Only)
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One matt finish passport-size colour photograph with white background.
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For Malaysian licence holders, an extract from JPJ Malaysia showing information of your driving record and licence information
And lastly, fill up the Conversion Form (Pink colored) once you arrive at the Traffic Police entrance lobby. And of course, do get a queue number upon entering the building.
Do ensure that you get all your documents ready especially the Entry and Re-entry Permit documents. I made two trips down because missing these 2 documents. The entry permit is important because they need to see if you obtain your driving license before or after you became Singapore Permanent Resident.Once all set, NETS payment of S$50.00 required on the spot for the processing fee. They do not accept cash payment. The officer will then provide the temporary slip for you and you are eligible to drive in Singapore now.
The physical driving license will mailed to your mailing address stated in the form in 10 working days.
For Singapore Citizens and PR, the new Singapore Driving License will be valid for life and there will be no need for any renewal.
TIPS: (a) If you are converting to Singaporean but yet to convert your foreign driving license on time, fret not. You need to prepare the documents as mentioned above and also additional documents including your rennouncation letter from Malaysia Embassy, letter from ICA after u submitted your rennouncation and also the warranty letter stating your nationality.
(b) If you obtain your driving license after you got Singapore Permanent Resident, the conversion procedures will be different.
For more detailed updated information on Traffic police and driving license you can check the traffic matters here or call them to find out more.
This is purely based on my driving license conversion journey experience. Any new updates, please check with the respective authorities for better understanding.