She took the seat in May after her predecessor Tracy Brabin became the first elected mayor of West Yorkshire.
Batley and Spen was previously held by Ms Leadbeater’s sister, Jo Cox, who was murdered in June 2016.
Ms Leadbeater told the PA news agency: “It’s been a fairly crazy few weeks in this new job.
“It’s a new world, Westminster is a very different world to Yorkshire and the constituency I represent, but one of the reasons I put myself forward was to bridge the gap between those two worlds.
“Hopefully the energy and enthusiasm I have to make a difference to the area that I love will stand me in good stead.”
She added she had had a “wonderful few weeks” meeting constituents, and said there was a “mixture of issues” to be resolved in the local area.
“I’ve been extremely well supported by my colleagues within the Labour Party, who have been extremely kind to me and also across different political parties as well,” she said.
“People who know me through my work on the Jo Cox Foundation have been extremely welcoming and friendly as well. I think that’s something that we need to talk a little bit more about, the cross-party work that goes on on issues.
“It’s been a rollercoaster few weeks, I’ve certainly been very warmly welcomed, and also by the fantastic staff that keep the Houses of Parliament going.”
Ms Leadbeater won her sister’s former constituency by 323 votes after a bitter and divisive campaign that many predicted Labour would lose.
The result came as a huge relief to party leader Sir Keir Starmer after a damaging loss in the Hartlepool by-election in May.