Like some tutoring and eldercare

INHOME

Think of services that happen at a person's residence rather than a facility, such as private lessons or assistance for seniors.

This clue hints at services that happen inside a person’s residence. "In-home" describes tutoring or eldercare provided at the client’s house instead of a separate location. The answer is a straightforward adjective phrase, not a pun or wordplay—just a literal term for where the service takes place. Think of it like "at-home" but with "in" instead.