Issues:
* Missing subject: "Kindly" is an adverb, not a verb. It needs a subject to perform an action.
* Awkward wording: "Let you know for further update" is unclear. It implies that you'll be letting someone know about an update, but it doesn't specify what action needs to be taken with that information.
Possible Corrections:
Here are a few ways to rewrite the phrase depending on the intended meaning:
* "Please let me know if there are any further updates." (Most common and direct)
* "Kindly provide updates as they become available." (More formal and direct)
* "Please keep me informed about any future developments." (More general and polite)
Example:
Instead of "Kindly let you know for further update," you could say:
"Please let me know if there are any further updates regarding the project."