。
She took my hand and gripped it tightly.
Literal
She [topic-は] my hand [object-を] took, and-then that hand [object-を] tightly gripped.
そして functions as an explicit 'and then' connector — relatively rare in casual spoken Japanese, where the te-form alone usually does the same job. Its presence here adds slight narrative weight, treating the two actions as two distinct beats rather than a single fluid motion. 握り締める is a compound verb (握る 'grip' + 締める 'tighten') — Japanese frequently builds emphasis through such verb stacking. The repeated demonstrative その手 (instead of just それ or omission) keeps the focus visually on the hand itself.