button-up
She said the man was wearing a buttoned-up blazer.
Black is everywhere this season, and styles are decidedly buttoned-up and puritanical.
The photo shows the children wearing buttoned-up school uniforms, their hair neatly brushed.
She has a reputation for being buttoned-up in interviews.
He is a buttoned-up Brit whose mouth hardly moves when he speaks.

SMART Vocabulary: related words and phrases

Style & appearance of clothes
aesthetic
alterable
anti-fur
Aran
backless
flouncy
foppishly
form-fitting
French tuck
frilly
reversible
ribbed
ribby
ruche
ruched
voluminously
voop neck
waisted
washable
wasp waist

You can also find related words, phrases, and synonyms in the topics:

Shy and modest
Manners & levels of formality