All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the hair clip is used at the top of the head or on its sides, then some scholars stated that it is included in the Hadeeth which you referred to in your question. However, if this is used at the nape of the neck, for example, then this is not included in the prohibition. Shaykh Saalih Al-Fawzaan said: “It is not permissible (for a woman) to increase the size of the head by gathering the hair with ribbons or buckles, whether this is done at the top of the head or on its sides, in a way that it becomes like two heads, as there is a severe warning to those who do so in a way that their heads look like the humps of camels . As regards the ribbons that do not increase the size of the head and are needed to adjust the hair, then some scholars are of the view that this is permissible.”
For more benefit on the statement of Shaykh Ibn ‘Uthaymeen on the ruling of tying the hair in a bun, please refer to Fatwa 123190.
Allaah Knows best.