Let me know how you are getting on.
How are you getting on in your new job?
If someone says the sentence above, it´s why he or she wants to know about your progress in your new job.
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How have you been? ( Present perfect )
It´s similar to "how are you?" - The interlocutor wants to know about you, about your life, a new job, a new activity or about what you have done lately.
PS: English is not my first language, but I hope it helps.