Place a saucepan over medium-high heat. Pour in the sweet tea, white vinegar, honey, dried chives, celery seeds, salt and brine from the banana peppers (reserve the banana peppers, refrigerated, until ready to serve). Heat until just boiling and the honey has dissolved, about 4 minutes.
Place the green beans in a heatproof dish or container. Slice the mini cucumbers into 8 spears each and add to the green beans. Pour the hot brine over the vegetables and set aside for at least 20 minutes.
Allow the pickles to cool completely before serving or storing in an airtight container. Serve with the banana peppers.