Here are two ways to correct the tense shift:
Option 1: Keep both verbs in the present tense.
* The author researches her subject before she writes a first draft.
Option 2: Keep both verbs in the past tense.
* The author researched her subject before she wrote a first draft.
The best option will depend on the context of the larger piece of writing. If the sentence is part of a larger discussion about an author's general process, the present tense is likely more appropriate. If the sentence is describing a specific instance in the past, the past tense would be better.