Hilchos Bikkurim 10:1

There is a Torah obligation to give a kohein first shearings, as per Deuteronomy 18:4: “The first shearings of your flock you shall give to him.” Leviim are obligated in this matter, just like Yisroelim. Under Biblical law, there is no minimum for these shearings, but by Rabbinic enactment one should not give less than one-sixtieth. Like first grain, this mitzvah applies in Israel, regardless of whether or not the Temple is standing. This mitzvah only applies to secular animals, and not to sanctified animals.

Hilchos Bikkurim 10:2

Pursuant to the previous halacha, let’s say that someone consecrated animals to the Temple and then sheared them. One might think that he must redeem the animals and give the first shearings to kohanim. Or, if someone consecrated an animal except for its shearings, one might think that he must give first shearings. The verse cited above says “your flock,” from which we see that this obligation only applies to one’s own animals.