Advocate Manzill Murshid, on behalf of Human Rights and Peace for Bangladesh, filed the writ with the HC bench concerned.
The hearing on the writ is likely to be held on Wednesday at the HC bench led by Justice Moyeenul Islam Chowdhury.
Manzill Murshid said the Road Transport Act-2018 was enacted on October 8, 2018 and it was supposed to be made effective through issuing a gazette notification.
On April 10 this year, he said, a legal notice was sent to the authorities concerned asking them to issue a gazette within seven days.
However, the government is yet to issue a gazette in this regard.
The writ also sought directives to issue a rule asking the government to explain as to why the authorities concerned should not be ordered to issue a gazette notification for making the Road Transport Act-2018 effective.
Secretaries concerned to the President, Prime Minister Office, Public Administration Ministry, Home Ministry, Law Ministry and Road Transport, Bridges Ministry and Cabinet Division have been made respondents to the rule.