As a support, Relic Shield is an obvious choice because is it made for melee support.
As a top lane, starting with Corrupting Potion will allow effectively trade with your opponent. Thanks to its burn component, you can come, stun, then walk back and take a nice chunk of an opponent's health, while possibly healing from minions and restoring some mana. Versus harder match-ups, Doran's Shield is the way, and for easier - Doran's Ring.
Iceborn Gauntlet is very effective and must be taken when going offensive. Not only it greatly increases damage dealt with Shield of Daybreak, but also combines well with high base attack damage and causes you to slow opponents hit and, if at full cooldown reduction, stick to them like nothing. Also it grants itself cooldown reduction and armor, which both are stats Leona needs.
Abyssal Mask is another offensive item - since she deals magic damage with all of her abilities, increasing it by 10% while gaining great defensive stats seems to be a good deal.
Dead Man's Plate furthermore increases the ability to stick to targets. It's hasting component allows for easier Shield of Daybreaking your opponents. Even if it's slow component wastes in most situations, it's very good item to afford.
Titanic Hydra is effective on all tanks that want to deal damage and Leona is no exception here. When having another item granting health, this can deal great amount of damage - by attacking, then Shield of Daybreaking, and then hydring, all in a quick succession, you can deal vast amount of damage.
Frozen Heart is effective when facing enemies depending on attacks. But if you have reached the cooldown reduction limit with other items, try Randuin's Omen instead. Having both is recommended when an enemy has two hypercarries, like an ADC and Master Yi or Tryndamere.
Righteous Glory allows for easy initiation, allowing you to save Zenith Blade for catching up escaping enemies. It grants health and armor to endure longer and mana and cooldown reduction to cast your abilities more.
When mostly supporting, Knight's Vow is the way. It allows you to assist your ally and get some wanted healing, while also decreasing damage they take.
Leona's Solar Flare has a short cooldown, reaching down to 33 seconds. When fighting her, always assume she has one ready.
If possible, try to focus other team members. Leona, being a tank, can absorb loads of damage, increased even more by Eclipse, but can deal lock on one target at max with her Zenith Blade and Shield of Daybreak.