The phrase "to reach high standards" means to strive for or achieve excellent performance or quality in something that is expected or required. Full definition
Together they created a vision to reach high standards of excellence in conjunction with a meaningful professional development for teachers. (idra.org)
That said, its story and characters don't reach the high standards set by the previous title. (metacritic.com)
She strives to validate their stories and support them to reach high standards through culturally relevant, language - rich pedagogy. (ellstudents.com)