continue, carry on, succeed
續 centers on keeping something going without a break: continuing an action, carrying on a task, or succeeding to a position or role.
續 combines 糸 (thread) with 賣, which likely contributes the sound and the idea of connecting or linking. The thread component suggests continuity, like fibers spun together into an unbroken strand.
The left side 糸 is thread, and the right side 賣 looks like a complex linked structure. Picture a thread running through the whole right side, tying everything together into one continuous line.
For ゾク, imagine a zoku (a made-up word for a long, unbroken chain) of thread: zoku -> ゾク, and the thread keeps the chain continuing without end.