'advance efforts' is correct and usable in written English.
You can use this phrase to refer to attempts made by someone to make progress on a particular issue or task. For example, "The government has taken the lead in advancing efforts to reduce carbon emissions."
Such approaches will further advance efforts toward establishment of applicable and effective biofuel production methods.
"I will use all the powers of this office to help advance efforts aimed at preventing more tragedies like this".
Our work will advance efforts to design a metabolically efficient platform strain for potential use in producing chemicals from lignocellulose.
City officials said the information should advance efforts to increase the city's reliance on solar power as part of its energy mix, reducing the metropolis's greenhouse gas emissions.
The results of this investigation serve to advance efforts to reduce the impacts soil erosion in the region and prevent further erosion in areas having high erosion sensitivities.
This access would reduce the region's energy prices from where they would otherwise be and would advance efforts to improve regional air quality.
Richard L. Berke, an assistant managing editor who oversees The Times's politics coverage, calls this advance effort "the most ambitious fact-checking we've ever done".
Such a game requires advance effort by a nonplaying volunteer who must prepare a set of deals that have been previously played.
We're also advancing efforts in less-invasive techniques.
Satellite imagery of small-scale farming around the globe, for instance, is rapidly advancing efforts to improve crop productivity.
He has focused on advancing efforts to translate iPSC-derivatives to assess their diagnostic and therapeutic potential for clinical translation.
