The phrase "to save up" means to put aside money or other resources over a period of time in order to accumulate enough for a specific purpose. Full definition
They also save up money for a rainy day, month, or year, because if being an author is your profession, rain will be in the forecast. (authormarketinginstitute.com)
Inventory shortages will continue to drive up home prices and serve as a barrier for first - time homebuyers, many of whom have a tough time saving up enough for a down payment. (reimag.co.za)