Ladies who have long hair have to tie their hair back.
この場合、次のように言うと良いですよ。
ーLadies with long hair have to put their hair up.
「髪の長い女性は髪を結ばなければいけない」
to put one's hair up と言い、to put up one's hair は不自然です。
ーLadies who have long hair have to tie their hair back.
「髪の長い女性は髪を後ろで結ばないといけない」
to tie one's hair back も to tie back one's hair とは言いません。
ご参考まで!