"further develop interest" is correct and can be used in written English.
It means to increase or enhance one's interest in something. Example: Our goal is to further develop interest in science among young students by organizing interactive demonstrations and workshops.
Barnard also used her grant to meet with Wellcome Trust-supported projects involved in the hearing voice movement, which examines the stigma around hearing voices and aural hallucinations, as well as further develop an interest in the science of memory, an idea first explored in her celebrated documentary on the life of playwright Andrea Dunbar, The Arbor.
And when he was himself exiled in the United States during World War II, he further developed his interest in American Indian and Inuit art, which also joined his collection.
In elementary school, she became intrigued by math, a subject that further developed her interest in chemistry.
Dale then moved to Norwich in 1990 with other PBI staff to form part of the John Innes Centre, where he further developed his interest in the environmental and food safety of GM crops.
In later life he further developed his interest in botany (where his work proved influential in England via his letters on the subject to the Duchess of Portland) and in music, as he met and corresponded with the operatic composer Christoph Gluck.
At Yale, he further developed an interest in literature, often neglecting his other studies.
After working on her first fragrance S by Shakira, Shakira further developed an interest in perfumery and wanted to explore more scents, saying "After working on my debut scent, S by Shakira, I became interested in the possibilities of expressing emotions through scents".
All these activities facilitate knowledge transfer, exchange of information at regional, national and international levels and involve academics, researchers, experts and service providers to further develop their knowledge and interest on hydrogen energy technologies in Turkey.
The applicant should demonstrate that the gap year will add to her value as a student at that college by enabling her to further develop her passions, skills, and interest in a particular field that she will continue to pursue.
