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You cannot have it both ways. If the picture is a square layout and the frame is a tall rectangle, then you cannot have all the picture showing. That would be requiring 2 different aspect ratios at the same time.
It would be cool, tho, to take the pix into Photoshop, and apply Edit > Content Aware Scaling to it! It might fake it well enough to get away with it. Especially if you prepared a protective alpha channel to the important part of the image, then you could distort it taller while keeping the people in the picture looking correct.
What Mike said (again very well).
I would only add that depending on the image "look" you may want to make a selection
Then use that to protect that bit of the image when content aware scaling...
Just remember you will have to unlock your layer (even from the background) otherwise content aware scale will be greyed out if you try edit > content aware scaling.
Also if you provide us with the shutterstock link or a preview of the image with watermarks we can advise how better to achieve this... Or if as you said a Rectangular image would be better.
As there is no way to get a square image to fit a rectangular shape without losing image top and/or bottom when scaling to fit another option is to place the image as a square and then add another element to your InDesign layout e.g. a solid/tinted frame with text information. Or ghost the image to fit the whole space as a background with the solid version appearing in its entirety on top of the background image. That can be quite effective. I'm sure there's lots of ways to utilise up the remaining space while keeping the overall design attractive.