Imbue with Spell ability is a 4th level cleric spell that allows you to use a 4th level spell slot to give the target a bit of spell casting ability (such as giving your fight the ability to cast a level 2 cleric spell each day). This spell is permanent until the cleric cancels it, and the target can regain the use of the granted power every time the cleric regains spell slots for the day.
Until the spell is canceled, the cleric cannot prepare a new spell for that 4th level slot. So you are trading your 4th level slot for the target's low level slots.
Spellcasting contract is a series of spells that are similar to Imbue with Spell ability, but they go to higher spell levels, grants better spells to the target, and it has a contract (because it is asmodeus related). Additionally, the deal is sweeter for the cleric, because they are give an unholy bonus to attack/saves equal to the highest level spell the target can cast (so a fighter that gets 2nd level spells means that the cleric gets a +2 to attack/saves)
Lesser Spellcasting contract is a level 5 cleric spell. (I am unsure if hierophant mediums can cast it though since it seems like it might have deity restrictions)
My main question is this: how do these work with a medium that has used a hierophant spirit? What happens if the medium decides to go champion the next day?
Both of these spells allow the medium to 'eat up a slot' that is a higher level than what they can cast when just using their psychic spells (while they eventually get 4th level slots to match Imbue, they get 4th level slots at a far earlier level when using hierophant).
Does the spell still stay in effect? Does it prevent the target from regaining use of the granted spells until the medium uses hierophant? Does does everything get put on pause until the next hierophant use?
...can I use this to cheese out some unholy bonuses for my champion focused medium? Yeah- getting nice bonuses while giving an ally some spells seems fantastic if you aren't actually going to use those high level hierophant slots.