Yes, but you do not look on Instagram to do it. Instagram ads are Meta ads. They are bought through the same ad account and served by the same system, so they appear in the Meta Ad Library alongside Facebook ads, with a label showing which placements each ad runs on.
Instagram has no separate ad library of its own. Searching inside the app will not give you a competitor's ad set.
How to actually do it
Open the Meta Ad Library, set the country to a market the brand sells in, set the category to "All ads", and search their Facebook Page name. This is the step that trips most people: the library indexes Page names, not domains or Instagram handles. Typing a website address or an @handle returns nothing, and people conclude the brand has stopped advertising.
If a brand's Instagram handle and Facebook Page name differ, find the Page through their Facebook profile, then open Page Transparency and follow the ad library link from there. That guarantees you are looking at the right advertiser rather than a similarly-named regional Page.
Reading the placements
Each ad shows where it runs: Facebook, Instagram, Messenger, Audience Network. Most advertisers run identical creative across all of them, which is itself useful information. A brand that produces distinct vertical creative specifically for Instagram Stories and Reels is investing more seriously in the channel than one recycling a square Facebook asset.
The vertical formats are worth studying closely, because that is where the format constraints bite hardest and where the difference between a considered ad and a resized one is most obvious.
What you will not find
Organic Instagram posts are not in the ad library, because they are not ads. Nor are influencer posts, unless the brand has boosted them as partnership ads, in which case they appear under the creator's Page rather than the brand's. That is a common reason a brand looks quieter than it is.
And no spend or impressions, for the same reason as everywhere else: Meta publishes those only for political advertisers.