inherit, succeed, continue, patch, graft (tree)
継 centers on keeping something going across a break: inheriting a role, succeeding someone, continuing a line, or joining pieces together like patching cloth or grafting a tree.
継 is the modern simplified form of 繼. The older form combines 糸 (thread) with a phonetic component that also suggests continuation. The modern form retains 糸 and uses a simplified right side that visually contains 米.
The left side 糸 is thread, and the right side looks like 米 (rice) but with extra strokes. Imagine using thread to patch a torn rice sack so the rice keeps flowing: the thread continues the sack's job.
For ケイ, picture a key (ケイ) that unlocks a family inheritance: the key continues the legacy.
continuation; continuance; maintenance; persistence; going on
relay; hook-up
succession
inheritance; succession; accession
to take over (someone's duties, business, etc.); to inherit; to succeed to; to carry on (a tradition); to continue
taking over; handing over; transfer of control; inheriting; passing on the baton
to succeed (a person, to a position, etc.); to inherit; to take over; to follow
patch; patching
to inherit; to succeed; to take over
joining; joint
succession; accession; inheritance
transit (passenger); connecting (flight); transfer (ticket)
stepmother
heir; inheritor
relieving the (starting) pitcher
coupler; coupling; joint; splice
joint; seam; joining point
heir; successor
to pass down (a story) from generation to generation; to hand down
addition; extension; elongation