The word alistaría is the conditional form of alistar in the first person singular. There are other translations for this conjugation.
See the full alistar conjugation

alistar

¿Por qué se alistaría un adinerado ingeniero?.
Why would a wealthy engineer enlist?
Ah, sí. ¿Alistaría a su hijo en el ejército?
Oh, yeah, would you enlist your son or daughter in the Army?
¿Alistaría a su hijo en el ejército?
Would you enlist your son or daughter in the army?
No se alistaría en el Ejército.
He wouldn't join the army over here.
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