A "phase shark" is someone who hangs around with people in a lower phase than they are in the hopes of scoring with them when they finally have enough freedom to (reasonably and without breaking any laws) have sex. It is usually the guys who are guilty of phase sharking, due to them vastly outnumbering women in the military.
The term almost always has derogatory connotations. I suspect a lot of that comes from people who are jealous that they didn't think to start hitting on that hot 1st phaser sooner themselves.
It's somewhat akin to an upperclassman dating freshmen.
"Christ that guy is such a blatant phase shark!"