Starmer, who was elected as Labour leader over the weekend, has announced that Thornton Heath MP Steve Reed will take on the shadow local government secretary brief.
Meanwhile, Bristol West MP Thangam Debbonaire has been appointed as shadow secretary of state for housing. She replaces John Healey, who has been in the role since 2016.
In a post on her website, Debbonaire said she looked forward "to campaigning for strong housing policies that will improve lives across the country".
Debbonaire said she would support Starmer's approach of "constructive engagement" with the government.
Planning has approached the Labour Party, Reed and Debbonaire for details on who will take on the party's planning brief, but none had responded by time of publication.
The shadow planning minister brief has been vacant since Roberta Blackman-Woods stood down as an MP ahead of December's general election.
In other shadow cabinet appointments, former Labour leader Ed Miliband has been appointed as shadow business, energy and industrial strategy secretary; Jim McMahon becomes shadow transport secretary; and Luke Pollard becomes shadow environment, food and rural affairs secretary.