。
He gripped the rope tightly so as not to fall.
Literal
Fall-not-so-as-to rope [object-を] grip-tightly-did.
握りしめる is a compound verb 握る ('grasp') + 締める ('tighten') = 'grip tightly / clench.' Compound verbs in Japanese often pack a manner-modifier into a single verb form, where English would need an adverb. The subject is omitted; only context tells us it's a person.