For the source text click/tap here: Chullin 89
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Our Mishnah at the beginning of the perek states that the prohibition of eating the gid hanasheh applies both to unconsecrated and consecrated animals.[1]
The Gemara begins by noting that it would seem obvious that this prohibition would apply to consecrated animals, because there is no reason to think that the prohibition against eating the gid hanasheh should be cancelled by declaring an animal to be sanctified. Among the suggestions given by the Gemara to explain this halacha is that the author of the Mishnah might be of the opinion that a gid hanasheh has a taste and if cooked as part of the thigh it contributes a taste to the meat (Chachamim, 96b, 99b), and is not a just a tasteless nerve.
Accordingly, the gid of this animal was a prohibited item, and now that the animal has been consecrated there is an additional prohibition against eating and benefitting from consecrated meat.