Is it acceptable to wear new clothes (e.g., new sweater; skirt) on Sundays,Mondays, etc. or must new clothes always be saved for Shabbat?
It is perfectly acceptable. There is, however, an advantage to wearing them for the first time on Shabbos as then you are wearing new and nicer clothes on Shabbos (assuming that they are clothes that you will also wear on Shabbos and they are not only weekday clothes).
All the best