The back row forward has come into the side for Peter Buxton, who is rested after picking up a couple of knocks in the back-to-back victories over Worcester in the past fortnight.
Narraway is one of six changes to the 22 that beat the Warriors in the semi-final of the European Challenge Cup semi-final last Saturday.
Alongside Narraway, Jack Forster returns at tight-head prop in place of Gary Powell because of a shoulder injury, Jonathan Pendlebury and Adam Eustace swap positions at lock and there are also returns for both Olivier Azam and Adam Balding from shoulder and knee injuries respectively on the bench. Terry Sigley is also recalled because Forster is named in the starting line-up.
England international Mike Tindall will skipper the side in an unchanged backline.
Of the decision to include Narraway, head coach Dean Ryan told www.gloucesterrugby.co.uk "Pete Buxton will be rested because he has taken a couple of knocks in the last few weeks and we see this as an opportunity for Narraway to press his claim even further.
"Our back row is a very competitive environment, particularly with Adam Balding returning and Jake Boer not far away. This is Luke's first real chance to press his chances for the games until the end of the season.
"Jonathan Pendlebury's inclusion is rotational and Gary Powell has a shoulder injury. We have take time to gather some momentum following the Six Nations but with two victories against Worcester, we want to continue that form this weekend.
"It will be an extremely tough game against proud and determined opponents and we will have to be very focused to get the result we want."
Narraway's only previous start in the Premiership this season was against Northampton in March and he has made 16 appearances in all competitions - 11 from the bench.
Mefin Davies and Patrice Collazo are retained in the front row, while the back line is unchanged for the fifth successive match which means Ryan Lamb and Peter Richards form the half-backs and Anthony Allen links with Tindall in the centre.
Both James Simpson-Daniel (head) and Olly Morgan (leg) have recovered from knocks picked up last weekend. Mark Foster, who scored the winning try against Worcester, completes the three-quarters.
GLOUCESTER (v Leeds Tykes, Sunday, 2.30pm): Olly Morgan, James Simpson-Daniel, Mike Tindall (capt), Anthony Allen, Mark Foster; Ryan Lamb, Peter Richards; Patrice Collazo, Mefin Davies, Jack Forster, Jonathan Pendlebury, Alex Brown, Luke Narraway, Andy Hazell, James Forrester. Reps: Olivier Azam, Terry Sigley, Adam Eustace, Adam Balding, Haydn Thomas, Ludovic Mercier, James Bailey.
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