The 2021/22 campaign will be the seventh consecutive year Town have competed in League One.
And with the exception of one outstanding third-placed finish under Paul Hurst, Shrewsbury have ended five of the last six seasons sitting in the bottom half of the table.
Under experienced boss Steve Cotterill, though, there is hope Salop can again battle for a place in the Championship.
And former manager and defender King believes it will give everyone in the town a lift if they do manage to compete at the top end of the division.
“It’s time now for the club to move forward a little bit,” he said.
“They will have been in the division for a seventh season, supporters will get bored with that.
“They won’t want to finish seventh or sixth-bottom, they’ll think ‘here we go again’.
“Hopefully they’ll have a chance to get into those play-offs, more for everybody in the town.
“When you get in the play-offs the town is buzzing, everybody wants to talk about it. Maybe this is the year for them.
“If they get the quality players in they need, there shouldn’t be anything stopping them competing to go up.”
King also believes owner Roland Wycherley – who is one of the longest-serving chairmen in the Football League – will be keen to see Shrewsbury mount a promotion push next season.
“He (Wycherley) will be looking to get them up and promoted before he retires,” the former full-back added.
“He might be thinking of that soon because he’s been there a long time and done a good job with the finances.
“It’s one of the best-run clubs in that division by a country mile.”