If I have used "On the one hand", do I need to write "on the other hand" somewhere after?

The usual construction in the English (or any similar) language would be:

On the one hand... On the other [hand]... — Cambridge Dict.

"On the one hand I'd like a job that pays more, but on the other hand I enjoy the work I'm doing at the moment."

Sometimes, we do not explicitly state "on the one hand", but it is often assumed.

The following Google Ngram shows that "on the other hand" is used more frequently than "on the one hand".

On the other hand, using "on the one hand" without "on the other hand" will sound odd, or illogical, to a native speaker at least. There may not be any rules regarding this other than general usage trends.