"To promise a future" means to make a commitment or assurance that something positive will happen in the future. It is about giving others hope and trust in what is yet to come. Full definition
By advancing work in the field of early childhood mental health, we hope to build a more promising future for young children and their families. (perigeefund.org)
Please try make a prediction for my time frame, I have a very promising future in my past. (judithcurry.com)
Rather, it plays an important role in a dog's transition from the life they left behind to their new, often more promising future. (fohari.org)