Preface: I enjoy creating unconventional builds that have interesting and varied playstyle, preferably ones that make some thematic sense. So while I dont need super optimal character creation, I would like to make the most of what the classes can bring to the table.
With that out of the way, I actually think this is a fairly solid combination. One of the issues with Priest is that they spend so much time casting, if multiclassing you usually want either 1. To have a way to speed up said casting or 2. to have some action economy going, where theyre bringing passive value from the multiclass while Priest is occupied with their casting.
Some of the pros of a Priest/Ranger I can see:
The pet can be dealing damage and keeping the enemy occupied completely independent of what the Priest is doing
Ranger actually does have a speed buff in Evasive Roll, giving 10 seconds of quick at Class Lvl 3
Marked Prey (+10 ACC one enemy), Stalker's Link (+10 ACC on each pet-engaged enemy), and Survival of the Fittest (+10 ACC on enemies under 50% health) are (as far as I'm aware, correct me otherwise please) conditional accuracy buffs that stack, and apply to not just weapon attacks but spells also. There are a few ways to boost engagement of the pet like Champions Boon or that one Chanter chant, so you can even make Stalker's Link effect multiple targets thats a whole lot of spell (and weapon attack) accuracy.
All the Ranger's accuracy buffs and other passive ranged attack buffs provide the Priest with a pretty solid autoattack DPS when they're not casting
Priest+Ranger apparently has more story interaction triggers than any other combination, when choosing the right subclasses (Priest 25, Ranger 21, Magran 25, Ghost Heart 14). I dont know if any of these overlap or if they even bring any value gameplay/battle wise, but I thought it was interesting
There are naturally some downsides with all these of course, but overall the combination isnt too shabby compared to other Priest multiclasses.
Some thoughts on subclasses...
Priest of Berath/Ghost Heart - This sounds fun from a thematic point of view. Priest of Death + ghost wolf. Ghost Heart means you can fire and forget your pet at the start of battle without worrying about it dying and debuffing yourself. Touch of Rot does stupid damage for a Lvl 1 spell even if it has some limitations. This might be one of the few times the Greatsword modal might be useful (+30% damage for -10 ACC) with your overabundance of Accuracy buffs on a single target. Otherwise you can go into battle with one or more Arquebus/Arbalest, unload at the start, go on a casting spree, then summon your spirit Greatsword with a 31% corrode weapon lash to finish off single targets. I doubt Rot Skulls would be worth it still, maybe with the Ranger bounce and as a way to simply put a DOT on the enemy to buff pet damage?
Priest of Magran - Has a number of Priest-unique damaging spells. Ray of Fire + Ranger ACC bonuses probably works great, as does getting a crit with something like Shining Beacon (not unique to Magran but fitting for leaning towards fire). Torrent of Flame could be kind of hilarious using Evasive Roll to teleport into perfect position to blast enemies. Itd likely be much better to have Magran's Favor + Marux Amanth (or Sun and Moon) for spell PL boosting/echo chance, so unfortunately the ranged perks of Ranger would be a bit wasted...Although potentially the spirit weapon pistol + bounce + 31% fire lash + ACC bonuses + Gunner could be pretty solid damage? Also can just switch over to another weapon slot.
Priest of Skaen - for some reason I assumed Finishing Blow was melee ranged, but nope! I havent actually tested this, but Finishing Blow + Ranger Bounce ACC buffs should do a truckload of damage. Could even combine this with Hand Mortars or other AoE/bounce unique weapons too. Marux Amanth could even give it a chance to echo?
Arcane Archer - I didnt enjoy this subclass much last time I tried it, and if I remember correctly none of the spiritual weapons apply as Arcane, so your autoattacks would get an ACC penalty unless you had one of the specific unique weapons that have that property...and I completely forget which actually apply. That said, I guess with the right setup these abilities could be a great start of fight opening to pin down enemies, with imbue web/pull of Eora, then you could start piling on debuffs or damage while theyre immobilized, or fire off a Fireball, which with Ranger bounce + bounce from weapons could cause some chaos. Seeing as you spend so much time casting as a Priest, just dumping all your Bond points at fight start for big effect kind of makes sense. Magrans Favor in one hand + Fire in the Hole in the other would probably have the most synergy here, with the + to Fire PL and the extra bounce.
Priest of Woedica - not much here other than the fact the spiritual weapon is extremely strong. Not a ton of unique synergy with Ranger though other than all the ACC buffs...
Sharpshooter - When paired with a Hunting Bow with its -50% recovery modal, might be a pretty solid combo.
Anyways, Ill leave it at that. Look forward to hearing any more ideas I hadnt thought about. Thanks for reading!