Patrick Clancy's New Wife Rachel Danis Seen For First Time Since Lindsay's Mistrial

Lindsay Clancy looks like she has a real shot at freedom after her murder trial ended in a mistrial ... and if that happens, she'd probably be thrilled to do what Rachel Danis is doing here ... shopping for groceries.

TMZ obtained photos of Patrick Clancy's new wife perusing a Whole Foods in Midtown Manhattan on Tuesday ... the first time we've seen her in public since the shocking end to Lindsay's trial in Massachusetts.

It looks like Rachel just got done with a workout or a run ... and she's fueling up.

Patrick's better half wore a gray T-shirt, black workout shorts, and a highlighter-yellow fanny pack ... and we're told she ordered a to-go plate of chicken and string beans at the counter.

Folks who were there say Rachel was very calm while waiting for her food, and she kept to herself ... though people around her definitely knew who she was.

As far as we can tell, these are the first photos of Rachel published since Judge William F. Sullivan announced a mistrial in Lindsay's case Friday ... a shocking development, which her lawyer, Kevin Reddington, was none too happy about.

Prosecutors have not yet announced if they'll pursue criminal charges against Lindsay again ... but she could potentially walk free thanks to a legal principle known as "manifest necessity."

Patrick kept mostly quiet after giving his testimony in court ... though he and Rachel were spotted laughing and spending a ton of time together during the proceedings.

However, he's been more vocal since a mistrial was declared ... thanking the jurors and judge -- while also noting there will never be closure in the death of his kids, regardless of a jury's decision.

Patrick -- through a lawyer -- has also threatened legal action against online conspiracy theorists desperate to pin the death of his kids on him.