highly astonishing

He is highly respected.

to be highly pleased

to hightail it

to hike the prices/rent

to hike off the beaten track

it is hilarious

hilariously funny

up hill and down dale

hillbilly

He’s up to him

It’s up to him

Hindsight is 20/20

Hindsight is easier than foresight

by hindsight

I'm a Hindu.

to hint darkly at something

hip flask

hip

hire and fire [policy]

to hire a car

hire-purchase

to be hired on

on his own free will

His humor dried up