D&D Clerics' niche has in roleplaying terms been divine magic, and in practical terms healing. Wizard = fireball, cleric = cure wounds. Offense vs. defense. Done deal. As the game grew around them, clerics have declined in appeal vs. classes which can offer cure wounds PLUS turning-into-bears or cure wounds PLUS lockpicking.
But first you need to decide on the difference between arcane and divine. The best distinction I would impose is that divine power stems from the world, the universe/multiverse as it is, while arcane alters and warps its nature. As a side effect, this does paint divine as intrinsically shifted toward lawful and arcane toward chaotic, but if you look at roleplaying history (bards vs. paladins, for example) it does basically fit the class warfare narrative we can assume would permeate a magical world. After all, gods are already in power, large and in charge, making the rules by which others must live, and mages are nobodies trying to climb the magico-social ladder. It does also fit the cleric core function of healing, returning things to their proper function. Power over the afterlife (resurrection, necromancy) would still fall on the divine side of that line, if you assume afterworlds to be the nigh-absolute stomping grounds of divinities, where players can only operate with permission. It does also imply the abjuration school should be moved over to the cleric side, or at least that part that negates magic.
But even if you manage to settle that question, distinctions within the divine magic classes remain tenuous. The original cleric fit D&D's roots as medieval strategy wargaming, and was pretty solidly a christian-inspired priest with a license to kill. Druids as their pagan counterparts received a more slapdash treatment representing the wild days before organized religion, ignoring the word "druid" represents a culturally rooted priesthood in itself, which had less to do with wild animals than the passing of seasons and natural cycles. Shamans, if/when implemented, should have picked up the shapeshifting angle, but I'll deal with those classes some other time. Don't get me started on monks.
To resolve the overlap, I refer you back to my comments on prestige classes: either start with one basic class and branch out or establish clearly delineated base classes with less branching. A druid would be a cleric of Cernunnos/Freya/Hestia/Dionysus/whatever, but if you insist on keeping some divine spellcasting nondenominational, clerics themselves need to play up the worship angle to stand out. Very early in this blog I addressed their weird relationship to their deities, usually represented only as a spell battery to be tapped at the cleric's whim, as a talisman to be rubbed for spell-per-day, placing no restrictions and making no demands of the player. But if you're dependent for your mojo on some sapient cosmic entity, its personality should impact your own available choices!
If you notice me shifting the definition of clerics more towards paladin alignment restrictions, that's hardly accidental, but that and bards will come next time. I will say that I've never liked clerics' universal access to heavy armor, which segues nicely to my final point: god personalities.
I've ranted on this topic before. RPG gods tend to be rather dull, with rare examples shining for defining a range of proper action, not merely spheres of influence over the natural world. If clerics are to refocus on theistic worship as representatives of one personified cosmic force, then everything about them should be amenable to that deity's restrictions, from spells to armor to quest options. The "basic cleric spell list" needs to be severely truncated to separate spell domains more widely and shift availability to individual deities. Just one or two bonus spells don't really convey the difference between Poseidon and Set. Healing, while it should probably remain a cleric universal for pragmatic reasons, need not all be equal. There's room for slow regeneration, shielding, lifesteal, reactive healing vs. certain damage types, etc. The deities domains themselves should rule the efficacy of cleric magic, strengthening or weakening with weather, day of the week, time of year, terrain, or any other relevant factors. And if you really insist on chaotic deities, their clerics' access to magic should reflect that unpredictability, randomly becoming stronger or weaker or entirely unavailable from day to day, fight to fight or round to round.
In any case, while the cleric may not need to be entirely done away with like the fighter, still it cannot occupy the same broad category as it did when it was a quarter of the class list. As it no longer needs to be THE party healer, it should be less one class and more a divergent array of theistic praxis, synecdochical means of bringing a specific god along with the adventuring party. (Which, of course, means you need more interesting gods.)