New to crisis, how do I come up with an arc for a fictional character who barely appears on screen.

This is my first crisis. The guy has like one line and I have no clue what he wants or what his ‘end goal’ would be seeing as he serves no purpose in the source material. Any tips on coming up with an arc or ‘end goal’ beyond just ‘make it up’ (or at least going into depth on how I’m supposed to do that)?