Embolding Bond states......... "Each creature can add the d4 no more than once per turn. The bond lasts for 1 hour or until you use this feature again."      Does this mean that when my turn ends, I can't use the d4 on a saving throw if a creature cast a spell or effect on me?  Thanks in advance :)

Emboldening Bond from the Unity Domain cleric will allow you to use the d4 every turn.  So it will work on your turn, your teammate's turn, the monster's turn, etc....

You can review the following to get a detailed explanation of the difference between a turn and a round:

https://www.dndbeyond.com/sources/basic-rules/combat#TheOrderofCombat

Crazy useful, absolutely worth a 1-level MAD dip.  Doesn't even use your reaction, so that's still free for my War Wizard +4 to save.  Throw in Pally level 6 aura on my yuan-ti, and I'm unstoppable.

I thought you could only cast spells on someone else's turn as a reaction.  If the spell is an action or a bonus action, then I don't think you may cast it during someone else's turn.

Once per turn, add a d4 to an attack roll, a check, or a save.

You want to help your attack on your turn, or your getting an opportunity attack etc on someone elses turn?  Roll the d4.

An ability check required on your or anyone elses turn (grappling etc)?  Roll the d4.

Mob targets you with a save spell, dragon uses frightful presence, Dex save required to avoid something etc?  Roll the d4.