This is the 10487th most frequent Spanish word.
convencerá
"Convencerá" means "will convince."
Here 'convencerá' is used in a future tense construction indicating the act of persuading in the future.
Estoy seguro de que ella te convencerá para asistir a la reunión.
I am sure she will convince you to attend the meeting.
'Convencerá' is demonstrated here expressing the result of an action contingent on the condition being fulfilled.
Si le explicas bien tus ideas, convencerá al equipo de aprobar el proyecto.
If you explain your ideas well, he/she will convince the team to approve the project.
In this case, 'convencerá' indicates a confident prediction of the action of persuading.