The former Liverpool and England captain takes charge of his first domestic match as Rangers boss against Aberdeen at Pittodrie on Sunday.
Adam, who played alongside Gerrard at Anfield, is confident that his former teammate's "aura" and his signings could go on to stop Celtic winning an eighth consecutive Scottish Premiership title.
"They are going to be able to challenge Celtic," Adam told BBC Sport.
"The players that they're signing, the calibre of player they can attract because of who he is, his aura in the game, what he's achieved... all that is going to improve them.
"Man management is going to be crucial. They need to close the gap, simple."
The Light Blues finished 12 points adrift of Celtic and three behind Aberdeen in the league last season.