"To pursue that dream" means actively working towards achieving a goal or desire that you have. It means taking action, staying determined, and making efforts to make your dream a reality. Full definition
By pursuing her dream of becoming a model, she hopes that more women will be encouraged to embrace their burns and not let their scars hold them back. (health.com)
Changing careers may be a result of pursuing your dream job or a necessary act of survival while hunting for employment in a time of economic hardship. (work.chron.com)
They never let hardships or inequality prevent them from pursuing their dreams for themselves and their children. (educationnext.org)