The phrase "approach to advance" is correct and usable in written English.
It can be used when discussing a method or strategy aimed at making progress or improvement in a particular area.
Example: "Our approach to advance the project involves collaboration and innovative thinking."
Alternatives: "method to progress" or "strategy for improvement".
Madin, J. S. et al. A trait-based approach to advance coral reef science.
Challenge your current leadership approach to advance yourself, your team, and your organization.
We therefore expect this modelling approach to advance our ability to understand and predict the impacts of climate warming on polar bear populations.
The integration of thin metal fibers as well as carbon fibers (MCFRP) is a promising new approach to advance the mechanical properties of conventional CFRP-structures.
The system provides an approach to advance the study of multiple targets identified from gene array analysis with potential for characterizing gene expression signatures in clinical diagnostics.
The judge went as far as to praise the prosecution for having set up a "systematic approach" to advance the case through a succession of monthly updates related to the preparation of classified material for disclosure to the defence.
Its real value, though, lies in the "wisdom of crowds" approach to advancing and proliferating the best new techniques.
The satellite-feed performance is only the latest example of this artist's innovative approach to advancing his career.
Contrary to Norman Kiell's approach to advancing age, as an 80-year-old, I find that spending one's life is the more satisfying course.
This demands a lead being given from the top, and it also implies a less ideological approach to advancing public investment.
As one example, Greatheart Consulting has launched a Reciprocal Mentoring Lab, an approach to advancing high-performing women and equipping gender-savvy men.
