Price will pull on the number nine jersey against the Emirates Lions on Saturday afternoon and follows in the footsteps of former Warriors Mike Blair, Chris Cusiter and Andy Nicol, becoming the fourth Glasgow player in the professional era to be selected at scrum-half for the British and Irish Lions.
Meanwhile, tight-head prop Fagerson is set to make his first appearance on tour for Warren Gatland's side after being named in the bench.
He's first Glasgow prop to pull on the red jersey in 12 years, following in the footsteps of Euan Murray.
Fagerson had been due to start last weekend's win over Japan, but was forced to withdraw following an eleventh-hour knock.
British and Irish Lions team to face the Lions, Saturday 3 July 2021 (kick-off 5.00pm), Emirates Airline Park, Johannesburg
15 Stuart Hogg - captain (Exeter, Scotland)
1 Wyn Jones (Scarlets, Wales)
2 Jamie George (Saracens, England)
3 Kyle Sinckler (Bristol Bears, England)
4 Maro Itoje (Saracens, England)
5 Jonny Hill (Exeter Chiefs, England)
6 Courtney Lawes (Northampton Saints, England)
7 Hamish Watson (Edinburgh Rugby, Scotland)
8 Taulupe Faletau (Bath Rugby, Wales)
16 Luke Cowan-Dickie (Exeter Chiefs, England)
17 Mako Vunipola (Saracens, England)
18 Zander Fagerson (Glasgow Warriors, Scotland)
19 Iain Henderson (Ulster Rugby, Ireland)
20 Sam Simmonds (Exeter Chiefs, England)
21 Gareth Davies (Scarlets, Wales)
22 Bundee Aki (Connacht Rugby, Ireland)
23 Elliot Daly (Saracens, England)