I see multiple ways to do this. Paid Ads, Building a Featuring Account and building your own account with content creation.
1) Paid Advertisements
This is probably the most obvious way. Paying for people to see the photos of the artworks which can be presented in a video, photo or even photo set. There you can immediately link to shop the product. But I would actually link to a blog where you present the artwork individually. Showcasing the process that went into it. The artist behind the product - maybe even an interview. This way the piece gets a personality and is interesting even if the visitor decides not to buy in the end. From there you can link to an auction or sales page.
2) Featuring Account
Building a featuring account on Instagram is great to build an audience in a certain field. In this case, it would be about the kinds of artworks you are selling. Is it about paintings? Search on Instagram for artists sharing photos of their paintings and feature their content on this special account. This way you help them grow and they are more likely to link back to you and you are growing relatively quickly. This would require at least one upload per day. But ideally, you should share up to 5 reposts every day (and don't forget to properly attribute the artworks to the artists). This account itself is not - especially in the beginning - to just sell. It's to build an audience in your field. And from there you can link to your store. Or you can feature your own products every so often. I have seen people build such accounts up to 100.000 followers in less than 6 months. I'm pretty sure you can find some buyers in those numbers.
3) Building an Audience
This plays into the second part of the paid advertising answer. Building an audience by becoming a media company not an art selling company. Create interviews. Share the back story of artworks. Create a blog and link to it via Instagram and the other way around. People want to know more about art. How is it made? How can I do it myself? What is good art? And it's just a bonus if I am able to buy a piece as well. Instagram Stories is great to share your own process. Share insights with other artists. Let them show their process on your Instagram Story. Interact with other artists on the platform and build a community.
All these are just the beginning. There are endless opportunities. But I think it's important not to see Instagram as "I want to sell something now" but rather build connections and a following. And then interact with those people. Share your insights. And the works you are selling. Then people are much more drawn in and have a relationship with you and the work.
If you'd like, we can discuss this further in a conversation. I am very interested in these approaches and have built my personal Instagram account to over 25k followers.
Have an amazing day and enjoy the journey!