There are ten 6th-level spells in AD&D, up from the six that were in OD&D. Blade Barrier, Conjure Animals, Find the Path, Speak With Monsters and Word of Recall were all in OD&D as 6th-level spells. Animate Object was in OD&D as well, but named as Animate Objects. Aerial Servant and Part Water were there as 7th-level spells. The only brand-new spells here are Heal and Stone Tell.
Aerial Servant: Summons an aerial servant that can be sent to retrieve an object or creature. This spell description notes that there are consequences for the caster if the aerial servant is prevented from completing its mission; those aren't detailed here, but the creature's description in the Monster Manual says that it goes berserk and returns to kill the caster. The cleric also requires some sort of magic protective circle to summon an aerial servant in safety, and as I recall these are detailed in the Dungeon Master's Guide. (The cleric's religious symbol is also said to be viable protection, which seems a little too easy for my liking. How often is a cleric not going to have that on their person?)
A strength of at least 18 is required to resist being carried off by the Aerial Servant. The percentage chance of resistance is based on percentile Strength, which implies that only Fighters/Paladins/Rangers (and only exceptional ones at that) have a chance of escaping.
Aerial Servants gain a whopping four rounds of surprise against foes who can't see invisibility, and I'm pretty sure that this is the first indication that multiple surprise rounds are possible in AD&D.
Otherwise it's pretty much the same spell as in OD&D, only dropped a level.
Animate Object: Brings inanimate objects within the target area to life, and compels them to attack a target specified by the caster. The exact spell effect is vague: movement, attacks, damage, weaknesses, etc. are all left to the discretion of the DM, with a few examples given for the sake of comparison. It seems like a potentially good spell, but the ability to create a lot of relatively weak opponents isn't going to be much help when fighting more powerful monsters.
The spell in OD&D is similarly nebulous. The only concrete change is the duration (which goes from a flat 6 turns to 1 round/level), range (it's halved from 6" to 3"), and the area of effect. In OD&D, the spell affects a set number of objects based on their size; in AD&D, it affects an area of 1 cubic foot/level, presumably being able to bring to life any objects within that area. It's not entirely clear.
Blade Barrier: Sets up a barrier of whirling blades that deal 8d8 damage to any creature that tries to pass through. The barrier can cover an area as small as 5' square, or as large as 2" square. (Note the inconsistent use of the measurement symbols here; 5' obviously means five actual feet, whereas 2" is the game notation for 20 feet. Gary had a knack for making things needlessly confusing.)
To make things even more confusing, the maximum area of effect is said to be 20'x20' when underground, and 60'x60' outdoors. Correct me if I'm wrong, but doesn't the conversion of feet into yards when outdoors only apply to range? I was sure it's not applied to area, but this example seems to indicate that it is. (I just double-checked it, and I was correct. It's so important that Gary yells about it in ALL CAPS. So either this spell is wrong, or a special exception to the rule.)
This spell has some small differences between the AD&D and OD&D versions. The damage in OD&D is 7d10 rather than 8d8. The area of effect was up to 3" in diameter (seemingly creating a circular barrier rather than a square one). The range in OD&D was 6", but in AD&D it's been halved to 3". The duration was a flat 12 rounds, but in AD&D that's been changed to 3 rounds/level.
Conjure Animals: This spell summons a number of mammals whose Hit Dice add up to the caster's level. A 12th-level caster, for example, could summon one 12 HD mammal, or two of 6 HD, or any other such combination. The animals summoned attack the caster's enemies.
The spell is specifically worded to say that it summons mammals. So insects, lizards, birds, and fish are out. Technically, this spell should be able to summon humans, and a bunch of other monsters. What constitutes a mammal can get pretty nebulous once you start delving into the Monster Manual, but I'd limit it to mammals found in the real world.
The OD&D version of the spell allowed the summoning of one large animal (like an elephant), three of medium size (bear-sized), or six small ones (wolf-sized). The animals obey the cleric, rather than being restricted to attacking. So while the spell has become more powerful, it's now less flexible.
Find the Path: For the duration of the spell, the cleric will always take the correct path to reach his intended destination. It works outdoors and underground, and can even free the caster from a maze spell. The spell can be reversed as lose the path, causing the target (who must be touched) to always take the wrong path (it can be led by others, though).
The main difference between the OD&D and AD&D versions of the spell is the duration. In OD&D it lasted 6 turns + the caster's level, and would last a full day when outdoors. AD&D has seriously nerfed that, having a duration of just 1 turn/level.
Heal: Making its debut here is possibly the best healing spell in the entire game. It restores the target to within 1d4 of their maximum hit points, and completely cures disease, blindness and the feeblemind spell. That's potent, but perhaps not so potent as harm, the reversed version of the spell, which drains the target and leaves it with 1d4 hit points remaining. Harm requires a successful touch attack, but there's no saving throw, so it's definitely worth a shot against a tough enemy. I feel like this spell should have some sort of exotic material component to curtail its use, but there isn't one. It's a bit overpowered, innit?
Part Water: Creates a tunnel through a body of water, the size of which depends on the caster's level. The OD&D version of the spell had a fixed area for most characters, with only clerics of over 17th level being able to part a greater area of water.
Speak With Monsters: Allows the caster to speak with any creature capable of communication within the spell's area. The OD&D version of the spell had a duration of "3-12 questions", whereas AD&D gives it as 1 round/level, allowing whatever conversation can fit into that time (provided the creatures want to talk).
Stone Tell: This spell is appearing here for the first time. When cast on an area of stone, that stone will speak to the caster. The stone can give information about what has touched it, or what is concealed behind it (if anything). A drop of mercury and a bit of clay are required. Obviously this one's good for finding secret doors, or tracking. It has interesting implications regarding the sentience of inanimate objects, as well. Does everything in the D&D world have some level of awareness, and life?
Word of Recall: Instantly transports the cleric back to a predesignated sanctuary, with no chance of teleport failure. The higher-level a cleric is, the more stuff they can take with them (including living creatures) Basically, it's a one-way escape route for the cleric, and perhaps some of their friends. The example given is that a 15th level cleric can take 375 pounds with them, so unless you have a really small party and minimal gear there's no way to save everyone.
The OD&D version of the spell did not allow for other people to be transported (and didn't indicate whether equipment was allowed either, which I imagine led to some heated player/DM arguments.)