Ghost doesn’t provide any additional server-side scripting. However, if your site is behind Cloudflare, you can set up Cloudflare Workers, or you can use other serverless offerings. You could also set up a cron script that updates the post every X minutes (which is something I’ve done in the past).
I know it’s been a while and I’m not sure if you’ve found a solution to your problem but LightWidget has a pretty good reasonably responsive free instagram carousel. I found the free version to meet all my needs so depending on what you’re making you might not even need to upgrade but if you decide to it’s only a one time fee and not a subscription service
If you’re not editing the templates directly then you’ll need to put the code they give you in an HTML box in the CMS
I use LightWidget for my own blog, and for several customers - about 16 months smooth running so far - everyone seems happy.
You will need to fork out $10 if you want HTTPS - LetsEncrypt!
IMHO it’s worth it - of course, you can roll your own, including the Insta oauth infra etc - but I guarantee that will cost you more than $10 in time!