Gibbon Pass is very much Banff's hidden larch season gem as it's located in more remote area that is typically not accessed as a day hike. During the larch season, it is a sea of gold up there!

We personally hiked up to the pass when we stayed at Shadow Lake Lodge - one of the best backcountry lodges in Banff NP, but you could also stay at the Shadow Lake Campground. From there we hiked up to the Gibbon Pass, continued to the Gibbon Pass Peak (also known as Little Copper) and back down to the lodge. This made for a half day hike with a total 7 km and 700 meters of elevation gain.

To access Gibbon Pass and Gibbon Pass Peak as a day hike, there are two options:
1) via Redearth Creek Trail and Shadow Lake Lodge - 16.5 km one way (over 1100 meters elevation gain)
2) via Arnica Lake and Twin Lakes Trail - 11.8 km one way (around 1200 meters elevation gain)

As you can see, it would make for a really long day, but it is doable. You could also do this as a thru-hike if someone could pick you up on the other side!