Q. Is it better for someone to use the leftover unused olive oil from last year Chanuka, that was bought then, since it was already dedicated for the mitzva or better buy new oil to be used this year?
A. The fact that the oil was purchased for use during Chanuka, does not turn it into a chefetz shel mitzva or an object dedicated for a mitzva, that maintains certain restrictions. Therefore, the principle of "Once a mitzva was done with it, another one should follow" (Talmud Brochos 39b, Mishne Berura 297: 8, regarding hadassim from a lulav to be used as havdala besamim), does not apply to it, since the left over oil, was not actually used for lighting the Chanuka menora. Buying for the purpose of using it for a mitzva is only "hazmana lemitzva" and it does not have great effect (lav milssa hi. O.H.
677: 4. Biur Halacha D'H Hatzarich.
O.H. 638: 1 etc.).
Horav Shlomo Miller Shlit'a opinion is that if the old oil burns as good as the new oil does, it should be used this year, mainly because of considerations of not transgressing on Ba'al Tashchis or destroying or discarding something useful.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a