The couple were just short of a season’s goal of 80 points with a score of 79.97 after the first round of the competition in Tallinn, Estonia, putting them in fourth place. They will now skate in the free dance tomorrow, where they will be hoping to make up the three point gap between them and the third place couple, Italians Charlene Guignard and Marco Fabbri.
Two Russian pairs, Victoria Sinitsina and Nikita Katsalapov and Alexandra Stepanova and Ivan Bukin are in first and second place.
Historically, Gibson, from Prestwick and partner Fear have often performed better in the free dance, often moving up a place after the final skate.
Fear said: “That would be great, that would be a dream.”
Gibson added: “We go into the free dance wanting to do the best that we can and just really feel satisfied with what we do out there on the ice and if we go up a place, then that's amazing. But as long as we're really happy with what we've done, we’ll feel happy with that.”
The couple were drawn last to skate in the final group, which also contained the top three couples, as well as Sara Hurtado and Kirill Khaliavin from Spain.
Fear said: “Six years ago in our first Europeans, we were the first team to skate. So looking at that today and seeing that we were last to skate, just really put into perspective the progress we’ve made and it was just it felt like something to be really proud of.
She added: “We're really proud of that score as well. We're getting closer and closer to 80 which is definitely a goal of ours this season. So, to be so close is really satisfying and then also keeps us hungry to keep progressing throughout the season.”
Even if the couple retain their fourth place, it will be the best performance of a British ice dance pair at the European Championships since Penny Coombes and Nicholas Buckland won bronze in 2014.
Fear’s younger sister, Sasha Fear and partner George Waddell, who were second in this year’s British Figure Skating Championships, also qualified for the free dance in 16th place. It is the first time the couple have competed in the European Championships.
Fear said: “I'm so excited for her. I think she's just been having a blast so far this week. I remember my first Europeans and I'm so happy that she gets to experience this too.”