Ian Murray was recently appointed as Labour's shadow Scotland secretary.
The Dumbarton MSP defeated Glasgow councillor Matt Kerr by 10,311 votes to 7528 to win the role.
The legislation tabled by Scottish Labour MSP Monica Lennon is aimed at ending period poverty.
Scotland's only Labour MP has launched a bid to become the deputy leader.
Labour councillor Alison Evison will speak at the Local Government Association conference.
All the Scottish party leaders are out on the campaign trail ahead of Thursday's election.
Figures published by ISD Scotland show the number has increased by 55 on last year.
Neale Hanvey had been due to contest the Kirkcaldy and Cowdenbeath constituency.