You get to keep the temp HP after the spell ends now. Cool.

Do the temporary hit points stack from round to round?

Quote from Randicailin >>

Do the temporary hit points stack from round to round?

 Temporary hit points never stack, whenever you would gain new temporary hit points, you choose to either keep the old ones (and ignore the new ones) or take the new ones (and lose the old ones)

Honestly I think the biggest problem with this spell is the classes that get it. It's a solid spell, but maybe a bit niche depending on the campaign. I just feel that for Paladin you would never take this, especially since as a Half caster your spell slots are a lot more limited. As for Bard, it works better, and if you are pretty sure you will deal with frightened saves a lot, this works well, it's just that I from a gameplay perspective, I wish this was a spell you could have as a Druid or Cleric, where you can change spells on a long rest in the event the spell doesn't fit the situation. Flavor wise though this does feel like it mostly is limited to Bard and Paladin, as those are the "Inspiring" classes.

Let me share the way I read it:

"A willing creature you touch is imbued with bravery. Until the spell ends, the creature is immune to the Frightened condition and gains Temporary Hit Points equal to your spellcasting ability modifier at the start of each of its turns."

The willing creature can be me.

At the start of each turn, the touched creature gets +X temp hit points. 

The temporary HP points (not spent) are lost at the end of tue turn  and replaced by the new HP temp hit points.

Is that r to right?

Quote from 24TwentyFour >>

Let me share the way I read it:

"A willing creature you touch is imbued with bravery. Until the spell ends, the creature is immune to the Frightened condition and gains Temporary Hit Points equal to your spellcasting ability modifier at the start of each of its turns."

The willing creature can be me.

At the start of each turn, the touched creature gets +X temp hit points. 

The temporary HP points (not spent) are lost at the end of tue turn  and replaced by the new HP temp hit points.

Is that r to right? 

Yes, your understanding is correct.

Spells that target a creature can always be cast on yourself unless the spell description specifically says otherwise (e.g. if it said "you touch another creature").

The temporary hit points are essentially "refreshed" at the start of each of the target's turns back up to the original amount (your spellcasting ability modifier). They don't accumulate over time.