care about (someone's) success

Translations
заботиться о (чьём-то) успехе
A good mentor cares about their student's success.
Хороший наставник заботится об успехе своего ученика.
Definitions
To be genuinely interested in and supportive of another person's achievements, progress, or positive outcomes, often wishing for them to do well and feeling invested in their accomplishments.