Someone recently landed on this blog searching for "bible paragraphs mentioning Gabriel." I don't have anything specifically highlighting those, so I thought I'd make a quick note on it.
Gabriel is only mentioned in Daniel's vision in Daniel 8-9 and in the announcement of Jesus's birth to Mary in Luke 1. In Daniel, he's the one explaining to Daniel what his vision means. In Luke, he's the messenger giving Mary the news that she will be the mother of the Christ.
The specific verses are Dan 8:16 and 9:21 and Luke 1:19 and 1:26. The Bible only mentions two angels by name, if I'm remembering correctly, Gabriel and Michael.
Jewish literature from the Second Temple Period (between the Hebrew Bible and the New Testament mostly) have a lot more to say about angels, so there might be more specifically about Gabriel there. I don't have time to look at those sources right now.
I'm sure that the inquiry was probably inspired by someone looking for background related to the "Gabriel's Vision" inscription. If you're looking just for biblical passages, there's not much.