Emery will join the Gunners from Paris Saint-Germain, having guided the Ligue 1 champions to a domestic treble, and having claimed the Europa League title three times with Sevilla between 2014 and 2016.
However, despite the Spaniard's impressive track record, Parlour urged fans not to expect success overnight, noting that new managers often need time to implement their style of play.
Speaking at Arsenal's new kit launch, he said: ''You've got to be patient and give managers a chance. It doesn't change overnight. They will see the change in the team, in the first five games, but it will take time.''
''He'll probably want to get rid of a few players and bring a few more in. So I just hope he does get time, I'm sure he will because this has been a massive decision for Arsenal, as a club, to get the right man in.''
''I think it's a very good signing. Now, you have to stick by him and trust him, however way he plays. I'm hoping the fans do give him time - I'm sure they will.''
''On an ideal note, it would be great if they would win the first two or three games and really settle down, get everybody behind them. But it's going to be difficult to do that.''
He concluded: ''"It's a massive job for him and he's really looking forward to it. He's got so much energy, hopefully it will be the right fit for both parties."