buttoned-down
1. Having or fastened together by buttons, as of the collar of a shirt. Primarily heard in US, South Africa. We're going to a nice restaurant for dinner, so be sure to wear a buttoned-down shirt, please!
2. Conservative, unimaginatively conventional, or old-fashioned, as of a person's clothing, attitude, behavior, or beliefs. He spent his entire adult life as a buttoned-down clerk, so when he turned 65, he decided it was time for adventure!