I don't have time to read books.

Literal

Book [object-を] read spare-time [subject-が] exist-not-[polite].

本を読む is a dictionary-form verb phrase that modifies 暇 ('spare time, leisure') attributively — in Japanese, the dictionary form of a verb can directly precede the noun it modifies, acting as a relative clause without any connector. 暇 is a native-word noun for 'leisure, free time.' ありません is the polite negative of ある.