The word agobiará is the future form of agobiar in the third person singular.
See the full agobiar conjugation

agobiar

Si no se lo dices, te agobiará el remordimiento.
If you don't tell her, you'll never be able to live with yourself.
Si no pensamos en eso, no nos agobiará.
Doesn't have to bother us if we don't let it.
Sin embargo, pensamos que esta medida es una invasión de la intimidad y que va más allá, y agobiará a mujeres ya por sí vulnerables de una manera que resulta inaceptable.
However, we believe that this measure is an invasion of privacy and goes much too far, and it will burden already vulnerable young women in a way that is unacceptable.
No podía permitir que eso me agobiara.
I couldn't let it drag me down.
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