No, gifts for holidays and birthdays are only for family and maybe a few very close friends. It is probably a cultural thing - I have never heard of anybody in my country giving gifts or cards to professionals. I have sometimes received small gifts from students (not for Christmas though, and I would feel very awkward if I did get that), but only, I think from international students.

I have given my T a couple of things - a copy of a book I'd written, and a craft thing I'd made - but that had nothing to do with holidays. I don't think he would be legally allowed to accept anything valuable or expensive, because he is a public employee.