1 (be in favour) I think she'll approve creo que estará de acuerdo; creo que le parecerá bien; he's not allowed sweets, his mother doesn't approve no le dejan comer caramelos, a su madre no le gusta
yes, I heartily approve he knows what I feel for you, but I'm not sure he approves
2 (give authorization) dar su aprobación if Congress approves, the project will go ahead next year si el Congreso da su aprobación lo aprueba, el proyecto se llevará a cabo el año que viene;or
you can go, as long as your mother approves Japan might take part in UN peacekeeping operations if the Japanese Parliament approves