continue, carry on, succeed
纘 centers on the idea of continuing something that has been started, especially carrying on a task, tradition, or line of succession.
纘 combines 糸 (thread) with 贊, which likely contributes the sound and the idea of assisting or continuing. The thread component suggests an unbroken line, fitting the meaning of succession.
The left side 糸 is thread, and the right side 贊 looks like a complex assembly. Picture a thread being passed from one person to the next, continuing an unbroken line of succession.
For サン, imagine the sun (サン) rising each day, continuing its journey across the sky without fail, just as 纘 means to carry on.