A love story that unfolds between a mismatched pair — an elite prosecutor from a good family and a modern high school girl.
Literal
Good-family from elite prosecutor [and-と] modern-day female-high-schooler [called-という], unbalanced man-and-woman [possessive-の] between [in-に] unfold [passive-られる] love [possessive-の] story.
A book blurb or synopsis. 良家出身 ('from a good family') + エリート検事 ('elite prosecutor') vs. 今どきの女子高生 ('modern high school girl') — the contrast is the hook. アンバランスな is the loanword 'unbalanced.' 繰り広げられる ('to be unfolded, developed') is a literary verb often used for stories, battles, and dramas. The whole sentence is one long noun phrase — no main verb, just a book description.