The District would repeal a prohibition against surrogate motherhood, ban the practice of suspending preschoolers and make it easier for bicyclists and pedestrians to recover damages from motorists after accidents, under a few of the dozens of bills that D.C. Council members introduced Tuesday.

Most of the measures amount to reruns of progressive legislation that died last month when the council ended its previous two-year term.

But in reintroducing the measures Tuesday, several members enthusiastically predicted success this time, saying a younger and more liberal council appeared poised to embrace causes that had stalled in the past.

The newly elected Ward 6 council member, Charles Allen (D), for example, secured the co-sponsorship of every one of his colleagues for a measure to eliminate the threat of jail time and a $10,000 fine for couples who seek to have a child through a surrogate mother.

The measure, backed by many of the city’s most vocal gay rights groups, failed to reach a vote last year. Allen had worked on the bill previously as a council staff member and said passage would advance gay rights in the city by protecting women who choose to carry a fetus and couples who intend to adopt.

Allen called the District one of the five most restrictive jurisdictions nationally for surrogacy, a situation he said was “really out of step with our commitment to equality.”

The early and unanimous support for that and other measures highlighted a generational makeover underway on the council. The District’s 13-member legislature gave up a combined 64 years of lawmaking experience this month with the departure of five members, including Muriel E. Bowser (D), who was sworn in as mayor Friday, and Marion Barry (D), who died in late November.

Three new members joined the council Tuesday; two more will be elected in April to fill the seats of Bowser and Barry, in Wards 4 and 8, respectively. This week, Barry’s son, Marion Christopher Barry, 34, announced that he will run for his father’s seat.

It wasn’t just the council’s youngest members who introduced progressive legislation on Tuesday.

D.C. Council Chairman Phil Mendelson, 62, introduced a measure supported by the National Organization for Women that would allow women to obtain a year’s supply of birth control in a single prescription. Mendelson said the legislation “makes the use of contraceptives more likely because women who are unable to access birth control often forgo birth control all together.”

Council member Mary M. Cheh (D-Ward 3) took the baton from outgoing council member Tommy Wells (D-Ward 6), introducing a bill to reshape city insurance law. Her bill would make it easier for bicyclists and pedestrians to pursue claims against motorists’ insurance policies after accidents. Currently, bicyclists, pedestrians and others are prohibited from recovering damages from a motorist if their actions contributed in any way to an accident, such as a cyclist swerving without warning to avoid a road hazard.

Cheh said her measure was “one piece of a larger discussion” that the council needed to foster this year between drivers and the growing number of bicyclists about how to safely share the road.

David Grosso (I-At Large), the new Education Committee chairman, also revived legislation to prohibit public schools from suspending preschoolers, a practice that has increased in the District, which offers free classes citywide for 3- and 4-year-olds.

A report issued last year found that D.C. teachers had suspended 3- and 4-year-olds a total of 181 times in the 2012-2013 school year, Grosso said. “While I understand that at times children can be difficult,” he said, “I have a hard time understanding what behavior of a 3- or 4-year-old would constitute an out-of-school suspension.”

Grosso also introduced a bill that would require the District to hold “instant runoff” elections. Other cities allow voters to rank candidates in order of preference, with the votes of eliminated candidates reassigned until someone has a majority.

Grosso cited the forthcoming special election to fill the Ward 8 seat, which has attracted more than 20 candidates, as an example of why the legislation is needed. He noted that someone could win the Ward 8 seat with far less than majority support.

Council member Jack Evans (D-Ward 2) reintroduced a measure to ban the council from voting on city contracts. The bill attracted six co-sponsors, more support than ever before.

“To attack this pay-to-play culture,” Evans said, “we should go right to the source of the problem.”