Liam Hemsworth is getting back into the dating game, but he’s making sure he’s not in over his head this time.
On Thursday, Brown, 22, and Hemsworth were seen holding hands as they strolled the streets of New York City and enjoyed a meal at Sant Ambroeus in the West Village.
But, according to a source close to the actor, Hemsworth is not about to jump into a new serious relationship just yet.
“It’s very new,” the source tells PEOPLE. “Liam is taking it slow but he’s definitely interested in her.”
This is the first time Hemsworth has been linked to someone new since news of his split from Cyrus, 26, broke this summer.
He and Cyrus started dating after meeting on the set of the 2010 movie The Last Song. While they briefly broke up a few years later, they reunited and married last December in a surprise and intimate ceremony on their Tennessee property.
The actor spent time in Australia laying low after their breakup, mostly hanging out with his older brother Chris and his family. The duo was often seen surfing and walking around Byron Bay, where Chris, 36, lives with wife Elsa Pataky and their three kids.
Hemsworth has only addressed his breakup with Cyrus once: with an Instagram post after PEOPLE exclusively revealed the two had ended their marriage. He officially filed for divorce from the singer just days later.
“Hi all, Just a quick note to say that Miley and I have recently separated and I wish her nothing but health and happiness going forward,” Liam captioned a shot of a beach sunset.
She and Simpson, 22, have been sharing a slew of cuddly, romantic social media posts together lately, with their most recent one coming on Wednesday as Cyrus returned home from the hospital following her tonsillitis surgery.
While fans have begun to question whether Cyrus is moving too fast with Simpson, the singer doesn’t appear to be fazed.
“I know the public feels invested in my past relationship because they felt like they saw it thru from the beginning,” Cyrus wrote on Instagram, referencing her relationship with Hemsworth. “I think that’s why people have always felt so entitled over my life and how I live it because they’ve watched me grow up.”
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“But I am grown now and make choices as an adult knowing the truth/details/reality,” she said, pointing out that if she were man, she probably wouldn’t be receiving the same level of scrutiny.
The songstress went on to let her fans and everyone else know that they should get used to seeing her dating, which she admitted is also new to her, as she was in a serious relationship with Hemsworth for most of her teens and early 20s.
“With the exception of a few breaks, which usually in those times I was working my ass off with not much R&R … and meeting/trusting people in my position is really tuff,” she wrote. “Don’t f—ing pity me, that’s not what I’m asking for. I have a great life I wouldn’t trade for ‘privacy’ but PLEASE don’t make this awkward for me!”