One of the biggest changes might come in rhetoric and communication style.
Cooper was shadow home secretary for seven years in two stints and also spent five years as chairwoman of the home affairs select committee. Some in Labour pushing for a harder line on immigration occasionally complained that her deep knowledge of the issues involved made her public comments too nuanced to embody public dissatisfaction.
Mahmood is likely to go another way.
That was definitely the sense from her first brief interview in the role on Monday, in which she repeatedly vowed to do "whatever it takes" to tackle illegal immigration, suggested she could withdraw visas from countries that do not "play ball" on migrant returns and embraced the potential introduction of ID cards - all in clear, plain language.
Mahmood, 44, has been an MP for 15 years representing a constituency in Birmingham, but it is only in the past two years that she has moved into front-line, high-profile roles.
After spending her first five years in Parliament in a range of junior shadow ministerial portfolios, she co-chaired Cooper's unsuccessful leadership campaign in 2015. She then refused to serve under Jeremy Corbyn, instead dedicating her time during his leadership to fighting those on Labour's left-wing from a position on Labour's national executive committee, to which she was elected by Labour MPs.
In 2021, at the lowest ebb of Sir Keir's leadership, she was brought into the shadow cabinet to take charge of Labour's election campaign infrastructure. Even in that job, though, she was pushing her party to get over what she called its "queasiness" about talking tough on immigration.
In an interview with the Times in 2023, she said: "In the commentariat, among very politically engaged people, there's a sort of assumption about who is motivated by immigration as an electoral issue.
"My constituency experience is that, actually, that's not got very much to do with race. I represent a very diverse constituency that's 70% non-white, and immigration comes up as an issue that my voters who are black or Asian and from other ethnic minorities want to talk about."
That is an argument you can be sure she will be making as home secretary in the coming weeks.
Whether she can address those concerns will determine not just her political fortunes but those of this government and prime minister too.