The Kingdom Hearts series spreads learning abilities across various methods (level up, progress the plot, defeat a boss, or complete some other challenge), but that comes across as not having one "standard" method in the first place. Though stat boosts come primarily through level-ups, so that might create an expectation that most character growth is from experience points.
Final Fantasy VII averts this at the start, granting characters new Limit Breaks through repeated combat, but to teach a given character their level 4 Limit Break, you'll need a special item. There's also the Enemy Skill materia; see Blue Mages.
The Limit Breaks in Final Fantasy VIII are like this. Squall's Limit Break availability is based on his equipped weapon. Zell reads magazines to learn finishing moves. Quistis uses certain items to learn skills. Rinoa takes her dog for a walk, and learns a new skill during the plot. Irvine can use different bullets based on what's in inventory. Selphie (technically) has all of her best Limit Break Magic available from the word go, but once you use the special ones once the show up more frequently in future.
The Overdrives in Final Fantasy X have this feel, due to the diverse nature of the party. Tidus and Lulu gain new Overdrives by using previous ones repeatedly and levelling up, respectively. Yuna only has one skill that she starts with, but gets new Aeons to summon with it during the plot. Rikku's overdrives are based on the party's inventory. Auron levels up by collecting movie spheres, Kimahri learns Overdrives from enemies, and Wakka plays Blitzball. One of the most Egregious example of Guide Dang It would be Valefor's Energy Ray attack. How do you obtain it? By talking to a friggin' dog in the very first village
In Final Fantasy XIII, most skills (including basic Attack) are represented by nodes on the Crystarium. The exception is the characters' Eidolons, which are obtained during the storyline and stored in the inventory.
Ramza's skillset gets larger over the course of Final Fantasy Tactics. There's also the Ultima spell (learnable only by Ramza and Alma, and only during two storyline fights) and the Zodiac summon (learnable only by summoners, during one optional fight), which are taught by being hit with (and surviving) the skill in combat, as opposed to most skill which are purchased with JP.
In Persona 4 Golden, every party member gets a unique skill that is obtained through talking to them on a certain date after maxing their Social Links.
All the party members have social link skills. Golden also adds "Bike Ride" skills, which allow the party members to learn new skills late in the game by going on a trip to a spa with the protagonist.
In Digital Devil Saga, if you answer certain dialogue choices throughout the two games, Argilla, Gale and Seraph will automatically obtain the skills Seraph Lore, Pyrriphlegethon, and Reincarnate respectively when you reach the final dungeon.
Some of Ryuudo's most advanced special moves in Grandia II can only be learned after defeating his brother Melfis. Millenia, meanwhile, gains new special attacks from every piece of Valmar the party defeats.
In Chrono Cross very many of the ultimate or signature attacks are only obtained through doing a sidequest, some of which can be impossible to get if you don't make the right decisions during gameplay. In fact, getting the special ability for one character, Razzly the fairy, requires that you choose the worst option out of a quest in the previous disc and results in many innocent deaths (it's the tragedy that ends up empowering her).
In EarthBound, spells are acquired by leveling up, except for the two tiers of Teleport for Ness. The first Teleport must be learned from a talking monkey, and the second one is automatically acquired after completing the Magicant level.
In Clive Barker's Undying, all spells are acquired by taking a magic scroll, except for the Lightning spell. For that one, you must take a lightning rod and put it in a orifice on a roof. A lightning will strike the rod and you will receive the electricity, which will give you the spell.
ADOM is unique in regards to this trope. You only improve your existing skills by levelling up and the usual way to learn new ones is from NP Cs and wishes. However, mindcrafters and elementalists learn new Mindcrafting powers and new spells, respectively, upon level up.
In Dragon Age: Origins, each party member has a hidden perk tree of "Inspired" abilities, which are automatically unlocked at 25, 50, 75, and 100 Disposition and gave increasing bonuses to their primary character stats. If their Disposition to the Warden dropped, however, the perks were revoked. Wynne additionally had an active power Vessel of the Spirit, which was unlocked by certain story events.
In Knights of the Old Republic II, you normally learn skills by investing skill/feat points into them. However, you can only learn advanced lightsaber combat forms by receiving instruction from or fighting the Jedi Masters you find throughout the game.
Obsidian did something similar to the Dragon Age: Origins example two years earlier in Neverwinter Nights 2: Mask of the Betrayer, where increasing your Relationship Values with party members unlocked bonus feats (mainly skill and ability boosts applied to both you and the party member). Meanwhile the Storm of Zehir expansion has a list of Teamwork Feats which require two steps to unlock: meet requirements outlined in the game manual, then accept and complete a corresponding sidequest from the Adventurers' Guild at Crossroad Keep. All three games also give history feats for completing story requirements, and in SoZ some of them grant bonuses.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.