Hello and thanks for your question
Her father can apply for a contact order - but that doesn't mean that the court will make a contact order.
The court has to decide what is in the best interests of that partciular child, rather than which parent shouts the loudest.
It is government policy that children shoud have contact with the parent that they do not live with unless there is good reason why not - but in deciding whether or not that should apply in each case, the court must consider the welfare checklist in section 1 of the Children Act 1989, and that includes taking into account a child's wishes and feelings, bearing in mind their age and understanding.
The older a child is, the more wieght a court will give to their wishes and feelings, especially from the age of 12, 13, 14 upwards.
The child does not have to come to court. Their wishes will be put to the court by the Cafcass officer - so if your ex does apply to court, let the Cafcass officer speak to your daughter without you being there - so that there can be no allegation by your ex that you tried to infuence your daughter in any way.
As long as the court is satisfied that it is the genuine wish of your daughter - without any pressure or influence from you - not to have any contact with her father, the court will not make the contact order.
I hope this reassures you and helps, and I wish you the best of luck.
Thanks and best wishes...