deliver, submit, hand over
繳 centers on the act of formally transferring something to another party: delivering goods, submitting documents, or handing over an item.
繳 combines 糸 (thread) with 敫, which likely contributes the sound and may relate to the idea of binding or tying something for delivery. The exact historical development is uncertain.
The left side 糸 suggests thread or cord, and the right side 敫 looks like a hand holding something. Imagine tying a package with cord and handing it over to deliver it.
For シャク, picture a shack where packages are tied with thread and handed over for delivery: shack -> シャク.