"Best of luck for your future ahead!" - can this phrase be shortened to "Best of luck ahead!".
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"Best of luck for your future ahead" is a redundancy. The future is the time that lies ahead of this moment. So, there is no need to add that. Instead, you can say best of luck for the future or best of luck going ahead. I'd keep it simple and use the former.
No, "Best of luck for your future ahead" can't be shortened to "Best of luck ahead".
"Best of luck for your future ahead" combines a general phrase with a specific one: "Best of luck" is the general one and "your future ahead" is the specific phrase. So you could say all of these:
You can say "Best of luck" by itself or followed by a preposition phrase giving the specific situation you are wishing them luck for.