"The other day I was in a café and there were two fellas who were about 18 or 19 and they were literally like, 'You're a deadly actress', shouting it across the café," she laughs.
"It was so funny, they don't even start a conversation. It's always really positive. Like I feel so lucky, I'm getting to play a really deep and interesting human being on a prime-time TV show. I'm just getting lovely feedback from an audience of people - they are actually saying it to me on the street.
"It could be worse. Like, it's a nice thing to happen. I have kind of gotten used to it. Also, Irish people, we don't annoy famous people; we are kind of known for that.
"But I love the way a lot of the Dubliners, they just love Kin and love the kind of characters in it. They'll jump straight in and talk about a particular scene, but then they'll just like walk off and let you get on with your day."
Clare will begin filming the next series of Kin later this month and she is thrilled to be getting her teeth back into the role of grieving mum Amanda.
"She is kind of like Michael Corleone," she explains, referring to the famous Al Pacino character in The Godfather. "She kind of ends up pulled into it, even though she kind of doesn't want to be, but there's just that thing what happens her family. So it's really mad, a huge journey to play."
Next weekend also sees Clare fronting her hilarious self-penned play Sure Look It, F**k It, at the wonderful Beyond The Pale boutique festival near Glendalough, Co Wicklow.
"It's amazing. I actually can't believe I got to do it, I was absolutely delighted," she enthuses. "At first, we weren't sure because some dates may have been clashing, but then it all came together and I just got ridiculously excited because it's actually happening.
"I don't know about other actors, but I haven't done a proper live performance in three years now because of the way things went, with filming and working in different areas, and then the pandemic. I was absolutely starving for this side of performance."
The show is a magical, spoken-word odyssey through the streets of Dublin about Missy, a returned emigrant back in town after years of trying to 'make it' in New York. Clare, who has also written a couple of other plays and is an accomplished theatre actress, explains the background to her one-woman show.
"I have gone on a bit of a journey with it, because it kind of developed into a play over time because people kept asking about this thing that I had made up by accident at my uncle's 60th," she recalls.
"It's mainly about joy, and those moments in your life - like everybody has a moment where something goes wrong, big or small. You know the way with Irish people, [they say} 'F**k it', you have a cry and a moan, and look at whatever is going on.
"It's kind of that moment where you just shake it all off and you go: 'Step forward now, put my best foot [forward] now and do what I can with the situation.'"
Clare herself has made huge ground in recent years, getting the opportunity to get up close and personal with Hollywood A-listers such as Jake Gyllenhaal and Tom Holland, when she had a part in Spider-Man: Far From Home.
"Marvel are kind of cool because they keep hold of the tapes of actors that they think might suit the role, so it was very last minute when I got offered the role," she reveals.
"Obviously they had a massive budget, they are really good at what they do. I have met Jake Gyllenhaal before, but he was lovely. All the best actors are usually quite sound."
Joining that list of sound co-stars is Matt Damon, who she got to meet while filming The Last Duel. "With The Last Duel, I only really had a small role in that, but [Matt] was very nice.
"He came up to me and the other actors who were in it. He's exactly what you think, he's just a bit of a gent and makes an effort with everyone."
For more on Sure Look It, F**k It and the full festival line-up, see itsbeyondthepale.ie