Emperor Akihito has had to wait until the age of 85 and the passing of a special law to step down from his job, but for the rest of us, formal retirement typically comes in our 60s.
退職 (taishoku) is the common term used to refer to retirement, while the act of retiring gets suru treatment: 退職する (taishoku suru). The verb can also be used when you want to quit a job in general, though, so to be more specific just add 定年 (teinen, age of retirement) to make it clear that someone's career is coming to a close: 田中さんが定年退職するので、送別会を開きましょう (Tanaka-san ga teinen taishoku suru no de, sōbetsukai o hirakimashō, Ms. Tanaka is retiring so let's throw her a farewell party).
The kanji 退 has the meaning of retreating or withdrawing, and you'll also see it in media coverage of the Emperor's 退位 (taii, abdication) this week. Us common folk, however, have more chances to use it via the word 退社 (taisha). You'll see it on Japanese 履歴書 (rirekisho, resumes) tacked on the end of a company's name. However, in daily conversation the verb 退社する (taisha suru) can be used to mean both "quit a job" or to simply "leave the office" at the end of the work day.