Have to live with (something)
To have to endure something.Although the house is very cold we will have to live with it.
Hightail it out of (somewhere)
To run away from somewhere, to leave a place quickly.We decided to hightail it out of the restaurant and go home.
High time
To be time that something should already have been done.It is high time that we spend some time cleaning up our house.
In high spirits
To have much energy, to be cheerful.The students are in high spirits since their team won the tournament.
High seas
The ocean (away from the coast).The crew of the ship spent three months on the high seas before going to shore for a visit.
High and dry
Stranded, abandoned.They left the manager high and dry when they moved the company headquarters to Europe.
Hide one’s face in shame
To cover one's face because of shame or embarrassment.The man wanted to hide his face in shame after he lost his job.
Heart skips/misses a beat
Startled or excited from surprise or joy or fright.My heart skipped a beat when the truck almost hit us last night.
Heart of stone
Someone with a cold nature with no pity or warmth.The woman has a heart of stone and is not interested in how other people feel.
Heart of gold
A kind and generous and forgiving personality.My grandmother has a heart of gold and everyone loves her.