He said: "You've always got players in mind, you've got an ongoing list.
"You could have a list with mainly midfielders and strikers but Paul could say he wants a defender, so it's down to the specifics."
Chester, who had assisted Rangers boss Walter Smith's player searches since 2007, will be given the task of helping Lambert find players capable of strengthening his squad ahead of City's return to the Championship.
If he does well you'd be looking to him being involved in Scotland squads
Norwich City chief scout Ewan Chester on left-back Steven Smith
"Walter Smith and I worked together for many, many years at Rangers, and if you appoint a chief scout you trust him," said Chester.
"Paul will give me specifics and it's up to me to fill in the gaps."
One player Chester is familiar with is left-back Steven Smith, who came through the youth ranks at Ibrox but has signed a two-year deal at Carrow Road this summer.
"I've known him since he was coming into the professional ranks," Chester said.
"He's worked hard on the defensive side of the game. Originally he was a midfield player, his strength going forward speaks for itself.
"If he does well you'd be looking to him being involved in Scotland squads."
Source: BBC Sport