External fellowships exist for recent graduates in all fields and with a broad range of interests. There is also a smaller number of external fellowships available to current students. These fellowships are all highly competitive, but SLU students with a strong academic record and demonstrated interest in the fellowship's focus should certainly consider applying.
To maximize your chances of success, it is important to prepare well in advance (during junior year, at the latest), researching different fellowships, including their missions, terms, and qualifications, and talking with your academic advisor, any additional mentors in your chosen field, and the Associate Dean for Academic Advising Programs (firstname.lastname@example.org).
A list of some of the most prominent fellowships is maintained on the Research and Experiential Learning opportunities website, but note that this is only a partial sampling of the many options that exist: https://www.stlawu.edu/research-and-experiential-learning-opportunities/scholarship-fellowship-and-grant-information