The 21-year-old impressed as a late replacement during the first leg at Murrayfield and has been rewarded with his first start for the pro team.
Brandon Thomson drops to the bench to make way for Thompson.
Edinburgh won the first match 10-7.
Other changes in the backs see Robbie Fergusson replace Sam Johnson at inside centre and Rufus McLean come in for Ratu Tagive on the wing.
In the forwards, Oli Kebble returns at loosehead prop which should bolster Glasgow in the scrum, an area in which they struggled at the weekend.
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