The warm-up game, originally scheduled for four days, has been shortened to three days following an agreement between the two teams and will begin on Wednesday.
Gay had suffered a right-shoulder injury while playing for Durham against Middlesex in the One-Day Cup last week. He left the field after scoring nine runs off 17 deliveries. Although scans confirmed the injury and raised doubts over his participation, he has now been included in the squad.
The PCС Select XI squad also includes Shoaib Bashir and Matthew Fisher, while England Under-19 head coach Mike Yardy will oversee the team.
The first Test between Pakistan and England is scheduled to begin in Leeds on August 19.