My dependent who is a student and just got a job a few months ago, filed taxes this year. Can she still be claimed for the months before she began working?

Yes, if she meets the requirements to be your qualifying child or qualifying relative then you can claim her as dependent for 2021:

 

Qualifying child

• She is under the age of 19 (or 24 for full-time students).
  • No age limit for permanently and totally disabled children.
• She lived with you for more than half the year (exceptions apply).
• She didn't provide more than half of her own support for the year.

 

Qualifying relative

• She lived with you the entire year (exceptions apply).
• She made less than $4,300 in 2021.
• You provided more than half of her financial support.