Main Build: The primary build consists of Trinity Force followed by Lucidity Boots. Always choose Lucidity Boots for the ability haste, as they are the best boots for Gangplank. Trinity Force provides both attack speed and movement speed, making it the top choice.
Item Progression:

Trinity Force

Lucidity Boots

Infinity Edge (second item)

Collector or Mortal Reminder (third item)

Immortal Shieldbow (fourth item)

The recent buff makes Shieldbow feel amazing, and it’s recommended as a fourth item. It scales well, providing a 600-630 health shield. It’s comparable to or even better than Maw of Malmortius in terms of shield value.

Choosing Between Collector and Mortal Reminder:

Go for The Collector if you’re ahead and the enemy team is squishy.
Opt for Mortal Reminder if the enemy team has multiple tanky champions. Gangplank’s barrels already provide armor penetration, so the 5% extra armor pen from Lord Dominik’s Regards (LDR) is not as effective. Additionally, LDR no longer has the Giant Slayer passive, making Mortal Reminder the better choice for healing reduction.

Late Game and Situational Items

Serpent's Fang: Build Serpent’s Fang as a second item if facing shield-heavy compositions with champions like Ivern, Lulu, or multiple enchanters.
Bloodthirster: Against poke compositions, consider selling your boots for Bloodthirster to gain a significant health shield and sustain.
Youmuu's Ghostblade: Useful for mobility to move around the map and dodging abilities. It’s a great choice if you’re snowballing after purchasing Collector.
Opportunity: Great item if you are snowballing hard as well after purchasing Collector. If you don’t have to dodge a lot of abilities, opt for Opportunity instead of Youmuus.
Essence Reaver: Best used as a second item if you lack ability haste in your runes. It provides 70 AD, 25 ability haste, and 25% crit chance, making it a strong option for sustained damage output.