There is no clutch kit, just individual parts, as least that is the case for USA models and parts distributed in the USA.
So, this is a non-USA model, but you and the mower are actually in the US, correct?
The HRB536 was built in the same factory as its USA cousin, the HRB216, and I would
guess the blade brake clutch parts are identical. That said, I have zero access to official documents for the HRB536, so can't say for absolute the parts and the same for both models. Also, there were two different styles of blade brake clutch designs used on the HRB216, and maybe on the HRB536 too.
Finally, it may be a worn clutch, or the symptoms could be due to a worn, stretched, or out-of-adjustment cable as well. I'd check it first, and replace/adjust as needed. If that checks out, you need to disassemble the clutch and measure the lining thickness to confirm it is worn or not before replacement. A paper shop manual is invaluable for this level of service; but, again, the USA version of the document will be somewhat different than the European one. You can get a USA shop manual from Honda via eBay or Amazon:
Honda Power Equipment Shop Manuals on eBay
Honda Power Equipment Shop Manuals on Amazon