What is "nari"

what is “nari” means?
Domo Arigato for the reply

I am not a tutor but I will try to answer you this question.

Shakai -jin ni naruto , isogashiku nari , Eigo no benkyou o mattaku shinaku nari mashita .

NARI means "na ri ma shi ta. Soshite (=and) " or “na rimasu. Soshite (=and)”. It depends on the context.

So according to the text, we can say…

Shakai -jin ni naruto , isogashiku nari ma shi ta. Soshite , Eigo no benkyou o mattaku shinaku nari mashita .

But these sentences were too long, so the author shortened them.

In Japanese, there are many ways to shorten sentences or a sentence. We, Japanese speakers, write many sentences naturally without thinking too much…

If you want to know more, please wait for other tutors’ answers.

And what that “nari mashita” means? Does it needs to be repeated at the end of the expression?

なる (naru) means “become”, “turn into”.

なると (naruto) is なる + と(to). “と” after a root form means “if …,” or “once something happens” (causality).
Ex: If you go there… → あそこに いくと… (あそこ = there, いく = go).

なり (nari) is a connecting form of なる. Similar to “なって”, it forms a sub-clause meaning “because…”, “as…”, “being…”.

なりました is なる + ました(polite, past tense ending); る becomes り before ます or ました.

しゃか いじん に なる と 、 いそがしく なり 、 えいご の べんきょう を まったく し なく なり ました 。
( the break between しゃか and いじん is a typo. It should be one word with no break to mean しゃかいじん / 社会人)

しゃかいじん に なる と - if you become a member of society (i.e, adult citizen as opposed to a student).
…しゃかいじん (社会人) comes from しゃかい(社会; society) + じん(人; person)

いそがしく なり - “as you become busy”, or “becoming busy”, “getting busy”.
…いそがしい means busy(adjective), いそがしく its adverb form.

えいご の べんきょう を まったく し なく なり ました 。

…えいご の べんきょ - “study of English”, “studying English”.
…まったく - “seriously”, “in full”
…し なく なり ました - became “not doing…” → came to neglect… → neglected doing…
…し ない (don’t do, refrain) → し なく (adverbial clause) → しなくなる (came to not do…; neglected to…).

So in full, “Having become a member of society, becoming busy, I came to a state of not studying English diligently”.
More smoothly, “Once out of school, getting busy, I came to neglect study of English”