She arose
before she called Barak to do so (Judges 4:14), and he never actually arose.
Kuruvilla notes, This seems to be a strange case of the called person refusing to be raised up by Yahweh. One remembers that an element of the paradigm of Judges 2:11–19 missing here is the 'raising up'…of a deliverer by Yahweh (as in Judges 3:9, Judges 3:15 for Othniel and Ehud, respectively). Now we know why this item is lacking in Barak’s story—he, the deliverer, literarily (perhaps even literally) resists his being 'raised up.' So a woman has to 'arise' instead. Therefore, as Deborah declared for Yahweh, it would be a woman who would get the glory for this victory against Jabin.
1
9 And she said, “I will surely go with you. Nevertheless, the road on which you are going will not lead to your glory, for the LORD will sell Sisera into the hand of a woman.” Then Deborah arose and went with Barak to Kedesh.