If you mean "I'll contact you later about this matter", it should be "I will get back to you". )
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HUBLOTWould it be correct to say "get back with somebody" to mean "get back to somebody"?No. To get back with somebody is when you dated somebody, then split up and then start dating again. Mr Wordy gave you the correct answer. Note that it is more natural to contract the I will to I'll also.