Ayoola Erinle starts on the wing following his move from London Wasps, while the pack features fellow new faces Boris Stankovich, Benjamin Kayser, Marco Wentzel and Owen Finegan.
"There is a good squad here, as we keep saying, even with the World Cup boys away and I have huge belief in the guys who are involved," said Cockerill, who worked alongside Pat Howard in last season's Double-winning campaign.
Erinle joins Johne Murphy, Ollie Smith, Sam Vesty and Tom Varndell in the backline, with Andy Goode and Frank Murphy at half-back.
Julian White is named alongside Stankovich and Kayser in the front row, with Wentzel partnering skipper Louis Deacon at lock. Brett Deacon, Luke Abraham and Finegan comprise the back row for a traditionally tough fixture at the Memorial Ground.
"Of all the selection decisions, the back five in the scrum provided the most questions and I have gone for a balance there to play this weekend's game," Cockerill said.
"Owen Finegan gives us physicality and experience at a place where traditionally we have found it hard. Jordan Crane is unfortunate that he is the one to miss out, even though he has played very well. Marco Wentzel will also play his first league game for us and the balance between physicality and athleticism is the key for us."
The bench includes the experience of Mefin Davies and Paul Burke as well as England Saxons internationals Richard Blaze and Tom Croft.
Leicester Tigers (vs Bristol, away, Sunday, kick-off 3pm)
15 Johne Murphy
14 Ayoola Erinle
13 Ollie Smith
12 Sam Vesty
11 Tom Varndell
10 Andy Goode
9 Frank Murphy
1 Boris Stankovich
2 Benjamin Kayser
3 Julian White
4 Louis Deacon (captain)
5 Marco Wentzel
6 Owen Finegan
7 Luke Abraham
8 Brett Deacon
Replacements
16 Mefin Davies
17 David Young
18 Richard Blaze
19 Tom Croft
20 Christophe Laussucq
21 Paul Burke
22 Matt Cornwell
