Godman replaces David Blair, brother of Scotland and Edinburgh scrum-half Mike, in boss Andy Robinson's line-up.
David Blair has won praise for his displays at stand-off since coming into the side for his debut against Connacht last month but the 22-year-old drops out for the Ravenhill clash.
Head coach Robinson will hope to benefit from Godman's greater experience in a match against a side who are second-bottom in the 10-team league.
Robinson also selects centre Matt Dey in place of John Houston, who has a dead leg, and has urged the two backs to seize their chance.
The former England coach said: "The two players have worked really hard and therefore now when they are handed opportunities they have to take them. The key to getting into the team is when you are performing that you play well.
"It is hard for players when they are not getting the starts they probably would have got last year. But what is important for them is that they understand that by working hard they can get back into the team.
"Now they are in the side though it is not about them switching off, but instead pushing up some more gears in order to stay there."
Dey featured off the bench against Llanelli Scarlets last week while Godman has had to watch while the younger Blair brother has made a name for himself alongside his more esteemed, Scotland international, brother.
Ben Cairns replaced ankle injury victim Hugh Southwell at full-back, and Scotland prop Gavin Kerr comes in for Craig Smith.
Wing Andrew Maxwell gets the chance to face his former team as Simon Webster misses out with a back injury.