New Life in Chinese / Japanese...

This literally means “new life” or “new livelihood” in Japanese Kanji.

新生活 is most appropriate if you are starting a new career or otherwise are starting a new chapter in your life or a new beginning.

Note: This is not the most common word selection for a calligraphy wall scroll. But if you’re a westerner, you can bend the rules a bit.

新生 literally means “new life” or “new birth” in Chinese, Japanese Kanji, and old Korean Hanja.

Depending on the context, this word can also mean newborn, new student, rebirth, new birth, or nascent.
In Japanese, this can be the given name Wakaki.

Note: This is not the most common word selection for a calligraphy wall scroll. But if you’re a westerner, you can bend the rules a bit.

伊始 is a short version of “new beginning” or simply “beginning” in Chinese characters.

You can also translate this as “from this moment on,” “starting now,” or “henceforth.”

In the day-to-day speech, this word can apply to starting a new job, beginning a new career, entering a new chapter of your life, or taking a new position (in politics, scholarship, etc.).

新たな始まり is a Japanese word that means “new beginning” or “new start.”

Here's the character breakdown:
新た (arata) = new; fresh; novel; newly; freshly; or this can be like the prefix “re-” like “re-start” or “reset.”
な (na) is kind of a connecting article. This glues “new” to “beginning.”
始まり (hajimari) = origin; beginning.

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.

新的開始 literally means “new beginning” in Chinese characters.

The character means “new.”

The second is a possessive article connecting the ideas of new & beginning.

The last two characters can mean “to begin,” “beginning,” “to start,” “initial,” “commencement,” or “initiation.”