This was the second international competition of the season for the pair - who won a silver medal at the Autumn Classic in Canada two weeks ago - and marked a strong start to the season.
Both competitions are part of the Challenger series of International Skating Union competitions held ahead of the Grand Prix series at the start of the skating season.
Although the couple, who came 13th at last year’s World Figure Skating Championships, missed out on a medal at the Nebelhorn Trophy in Germany, their overall score was higher in both the rhythm dance and free dance sections than in Canada.
Skating a popular free dance programme to Vogue by Madonna, the pair achieved a mark of 113.43, which combined with their sixth place rhythm dance score of 74.82, came to 188.25 overall, propelling them into fourth place.
In Canada, their silver medal-winning place was achieved with a score of 184.09.
Gibson, from Prestwick, said: “We felt like we made progress at this event, performing better here in Germany and further polishing our programs.”
Speaking about the Autumn Classic, he added: “We are both extremely happy with our skates at this event and of course, placing second was a nice beginning to our season.”
Last year was considered to be a breakthrough season for the pair, who qualified for the free dance at the World Figure Skating Championships for the first time.
Canadian ice dancers Laurence Fournier Beaudry and Nikolaj Sorensen, who train with Gibson and Fear in Montreal, won the title at the Nebelhorn Trophy, followed by Americans Kaitlin Hawayek and Jean-Luc Baker in second place.
Current British female skater Natasha McKay, who trains in Dundee and has held the British title for the past three years, has had a disappointing start to her season, ranking 12th in the Lombardia Trophy in Italy - also part of the Challenger series - earlier this month after mistakes in jumps in both her short and free programmes.
Karly Robertson and Danielle Harrison, who also train at Dundee and have both held the British title on previous occasions, ranked 12th and 16th respectively at the Ondrej Nepela Memorial competition in Slovakia.