Yes, you can use the article when it is clear from the context which drawer or purse or whatever noun you are referring to.
I opened the drawer and there was a snake in it. The reader would wonder which drawer was being opened. I would use my drawer here for clarity.
I went into my kitchen, opened the drawer, and there was a snake in it. Now that the identity of the drawer is known, the article alone is sufficient.
Student or Learner