"She lived in New York last year."
去年 can be placed also at the beginning of the sentence, just before the subject. Please look at this explanation:
"Time words can appear in one of two positions in the sentence in Chinese: either at the beginning of the sentence (before the subject), or directly after the subject. The structures are:
Time + Subj. + Verb + Obj.
Subj. + Time + Verb + Obj."
Can someone add the other alternative, please?
Important: They're not really tense.
了 is about something being accomplished, which makes it an aspect particle.
会 is exactly like English 'will' or 'going to', a modal auxiliary.
(Yes, it's true: English technically has future modality, not future tense! Your grammar book lied!)