If the posts will be posted in the future, you can set up a Tracker. Trackers collect posts in real time as long as they're running. Trackers are available through a Union Metrics subscription.
If the posts were shared less than one month ago, then you can access them through a Tracker (in a Union Metrics subscription). A new Tracker will start with a backfill of 1,500 to 5,000 posts from the past month when you set it up.
If the posts were shared less than one week ago, you may be able to use a snapshot report. Free snapshots include up to 100 tweets from the past few days, and full snapshots include up to 1500 tweets. Both are capped at about a week of historical data.
If tweets were posted more than 30 days ago, that historical data is no longer available through any Union Metrics self-service subscriptions.