hang, suspend, depend, arrive at, tax, pour
掛 centers on attaching or connecting one thing to another: hanging or suspending something, depending on something, or arriving at a place. The tax and pour senses are extensions of applying or attaching an action to something.
掛 combines 扌 (hand) with 卦, which likely contributes the sound and the idea of hanging or suspending. The exact historical development of 卦 within this character is uncertain.
The hand radical 扌 beside 卦 suggests a hand hanging something up. Picture a hand placing a divination plaque (卦) on a hook to suspend it.
For カイ, imagine a hand hanging a kite (カイト) from a hook: kite -> カイ, and the hand suspends it in the air.
to take (a resource, e.g. time or money)
to hang up (e.g. a coat, a picture on the wall); to let hang; to suspend (from); to hoist (e.g. sail); to raise (e.g. flag)
device; contrivance; mechanism; gadget
seeming; pose; show; pretense; sham; mock
(on the) point of going out; (at the) moment one is about to leave
credit
to start; to begin; to commence
holding two or more positions concurrently
shout (of encouragement, etc.); yell (used to time or encourage activity, e.g. "Heave ho!")
replacement; substitution; rebuilding; changing
negotiations; bargaining
hook; gab
hold; catch
large-scale
to aim at
seat; bench
to begin (doing); to start; to set about; to get down to
installment; instalment; premium; bill
multiplication
to hang (something) on (something); to throw on (clothes)