The phrase "little drama" means that there is not a lot of excitement, conflict, or chaos happening. It suggests that things are calm, peaceful, or uneventful. Full definition
I have a skilled trade and stable with little drama looking for the same. (privateherpesdating.com)
This is just going to be about getting through the fixture with as little drama as possible. (football-bookmakers.com)
Like I said in my post, she did ask a few times after we were done, but it was only a few times and there was very little drama surrounding it. (attachmentparenting.org)