He has recently started his business. vs He recently started his business.

[Ahussain911]

Which one is correct?

He has recently started his business

He recently started his business

[Mister Micawber]

.
Both are fine. AmE often uses the second form.
.
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Native English teacher at Mister Micawber's

[Ahussain911]

Kindly elaborate

[Mister Micawber]

.
There is nothing to elaborate upon. Both are correct.
.
_________________
Native English teacher at Mister Micawber's

[Kitosdad]

:lol:
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Keep it simple ... Keep it interesting.