Biting, usualy on the neck, and the vibrating claws are usualy part of the mating routine. But can also be a sign of aggression.
If the female is less than 4-5 inches it may be more aggresion and less mating, too small to lay eggs, but some one more qualified may have to answer that.
I would think if this happened very soon after introducing the new turtle to the tank it is probaly trying to mate. it is that time of year.
Either way, if you plan on keeping them together. Be prepared to have a set up that has a nesting area. If the female doesn't have some were to lay the eggs they could become impacted and that is a very serious problem.
here is some good info that was passed on to me. one of the links may be dead i'm not sure which one. (can't test at work)
http://www.tortoisetrust.org/articles/Nestsites.htm
http://www.chelonia.org/Articles/Emerge ... niques.htm http://www.gctts.org/pmwiki/pmwiki.php/ ... lonianEggs
As always, spelling errors are complimentary.
Taylor Family Zoo:
2 Red Ear Sliders
2 Fire Bellied Toads
1 Bearded Dragon
1 Short hair Kitten
1 Long hair Kitten
1 Siamese Manx mix (stumpy tail)