The England centre joins Moses Rauluni and Kameli Ratuvou in the starting line-up with the Fijian duo back following their heroics in France.
With Saracens and Bristol both unbeaten, the winner on Sunday will have a great chance of progressing to the quarter-finals of the cup.
But Gaffney also has half an eye on the forthcoming Heineken Cup fixtures against Glasgow and Biarritz as Saracens target qualification from a favourable pool.
"We've rotated the squad again this week, which is something we have to do if we are to compete in all three competitions," he said.
"It's also important that those who are short of game time get some action.
"We face a series of big games in the next few weeks and we've got some guys on the bench who will get a run out at some point.
"Players like Andy need to get their eye in as he's been with England since June.
"He has been playing a different brand of rugby to that which Saracens play, so he will need a bit of time to adjust."
Bristol have kept faith with the pack that served them so well in the 18-11 victory over Llanelli in the opening round of the cup.
But there are changes in the backs with Jason Strange taking over from David Hill at fly-half and Brian O'Riordan coming in for Shaun Perry at number nine.
Bristol head coach Richard Hill said: "We tried a few different combinations for the last EDF game and we beat one of the best teams in Wales.
"It looks as though Saracens will be as strong as they can be and they'll believe a bonus point win against us will put them in the semis."
Wasps have welcomed back three of their World Cup stars for Sunday's clash with Gloucester at Adams Park.
England's Lawrence Dallaglio and Paul Sackey start at right wing and number eight respectively while France hooker Raphael Ibanez has been included on the bench.
All Black prop Clarke Dermody will make his London Irish debut in Sunday's showdown against the Ospreys, alongside former Springbok hooker Danie Coetzee and Tonga international Tonga Lea'aetoa.