If candlesticks are on a tray can they be moved off the table on Shabbat?
The candlesticks - if lit before shabbas and stay lit into shabbas - remain muktzeh and cannot be moved for the entire shabbas. (One may ask a non-jew to remove them if the place is needed).
If the tray is designated for the candlesticks then the tray is considered a bosis (base for mukzteh) and is muktzeh for the duration of shabbas. Even if the candlesticks were removed somehow the tray remains muktzeh and can not be moved.
See Igros Moshe here.