なさる (honorific replacement of する)
する → なさる
Irregular ます-form: なさる → なさいます (not ×なさります)
て-form: なさって
なさる is the honorific (尊敬語) form of する ("to do"). It is used when describing the actions of someone you wish to show respect toward, such as a superior, a customer, or an older person. You never use it to describe your own actions.
なさる is a godan (五段) verb, but it has an irregular ます-form: the expected なさります becomes なさいます.
なさる can replace する in する-compound verbs (e.g. 勉強する、旅行する、運動する) to make them honorific.
The imperative form なさい is used as a relatively soft command or instruction, often by parents or teachers speaking to children or students. This usage does not convey the same honorific nuance.
Another common way to form honorifics is お + V[stem] + になる (e.g. お読みになる). なさる is specifically the honorific replacement for する, while お~になる is a general pattern that works with most verbs.