How to preseve crop to next image shooting thethered?

Copy/Paste sounds like a better approach, if newly arriving images need the same edits repeated.

Unlike with Sync, you don't need to each time 'fetch' those same settings again.

They are continually held in memory, ready to be applied at will (with Ctrl+V / Cmd+V).

A Crop is one item you cannot include in a Develop Preset. (Develop Presets can be set in the Tether dialog)

Only work-arounds would be possible in LrC.

You could use a 'visual' overlay that will  appear on the 'full-size' image as it arrives from the tether.

This would act as a Guide for camera framing, so that you can Crop later in a manner similar to the overlay.

Not to forget that you can Batch Crop many images in the Library Grid view by selecting a Crop preset in the Quick Develop panel.

Here is an Overlay PNG image (Red border with central transparency) applied over an image.

Overlay PNG images can be created in Photoshop-

Hi there,

This might give you some good ideas to work with:

https://jkost.com/blog/2020/01/20-tips-for-cropping-in-lightroom-classic.html

Let us know if you need more help