Chris McEleny is standing for a second time after finishing last in the 2016 contest behind Robertson, Tommy Sheppard and Alyn Smith.
The nationalist’s group leader on Inverclyde Council told The National: “In 2016 I stood to make sure local government was at the heart of the debate.
“The reality though is that Angus Robertson was one greatest politicians of our time and it was that experience our members opted for,” he said.
“However this time round I believe that the experience I have gained since then, my left-of-centre beliefs, a position Tommy spoke to the last time round, as well as the work I have been doing since then as a Scottish representative of the EU’s committee of the regions, are all issues that speak to those that voted in the last election.
“In 2016 I aimed to shape the issues, this time around I aim to so we can get on with the job of taking our message to communities across Scotland.”
Mr McEleny joins economy secretary Keith Brown, Glasgow Cathcart MSP James Dornan and Julie Hepburn in the running to become depute leader.
Mr Brown previously stood for the role four years ago but lost out to MP Stewart Hosie.
The deputy leadership position became available when Mr Robertson stepped down in February.
Westminster leader Ian Blackford and several high-profile MPs including Pete Wishart, Johanna Cherry and Tommy Sheppard have ruled out putting their names forward.