Though the Gers would enjoy just one season in the top flight following the defender's arrival in 2011, the campaign before he signe had seen the club win the Scottish Premiership title and the League Cup, as well as reach the group stages of the Champions League.
And as Mark Warburton's men prepare for their first term back at the highest level after their dramatic fall into the bottom tier, Wallace has claimed that with the new signings that have been made this summer, the current crop have the ability to emulate what that team managed before the off-field issues.
"The lads coming in are having to get used to a new way of working and there is no reason why we can’t aspire to go on and do the things that those players did in their careers," he told the Evening Times.
"We have got young lads that are capable of going on to the highest level and, as a team, we want to aspire to get back to, for instance, my debut in the Champions League.
"As a group of players, staff and as a club there is no reason why we can’t look at the team that I came into and to aspire to get where they were and become champions. That is certainly our target."
With the squad that won the Scottish Championship title last season also beating three top flight sides - including Celtic - during their Scottish Cup run, it certainly appears that they have the potential to get back towards the top of the table.
However, they must now prove that they can get the better of those sides when they come up against them every single week.
But with the new signings bringing experience and quality, it appears that they are in with a good chance of emulating the team that Wallace joined and finally putting an end to their journey back to the top.