This phase II trial studies how well pirtobrutinib works in treating elderly patients with chronic lymphocytic leukemia (CLL). Bruton tyrosine kinase (BTK) inhibitors such as ibrutinib, acalabrutinib, and zanubrutinib work by blocking the action of the BTK protein that signals cancer cells to multiply. These are very effective, tolerable, and commonly used to treat people with CLL, but they may lead to drug resistance over time. Pirtobrutinib, also a BTK inhibitor, may work better in treating elderly patients with CLL.