Covic was one of the Wanderers' highest-profile players during his time there, the highlight coming last year when he was presented with the tournament MVP award as Wanderers made history by becoming the first Australian club to win the AFC Champions League.
Wanderers chose not to re-sign Covic, who has since turned 40, at the end of last season and now Redmayne and Dean Bouzanis are two goalkeepers in their mid-20s who are vying to become the number one at the club.
After both Redmayne and Bouzanis were given time by Wanderers coach Tony Popovic in the club's first two pre-season trial games, Redmayne played the full game in the 1-0 win over Brisbane Roar in an FFA Cup round of 32 match last week.
But it remains to be seen what Popovic does when Wanderers play their next FFA Cup game against Palm Beach Sharks at Cbus Super Stadium on Tuesday, 1 September.
Redmayne would obviously love to go around again in that match and be the first-choice goalkeeper for the A-League competition kick-off in October, but he is taking nothing for granted based on one appearance in an FFA Cup match.
He sat on the bench without being used in two winning grand finals for Brisbane, behind Michael Theo, so he knows what it is like to get close to what you want without being able to touch it.
"I'm thankful to have been given the chance in the FFA Cup match and now I've just got to keep working hard," Redmayne told The World Game.
"That's all that matters.
"If you get a chance you've got to take it, but I'm not reading anything into what has happened so far. It's still two months until the season proper starts, so I'm just going to keep working hard and see what happens.
"I'm one of three goalkeepers we've got at the club (including the youth-team 'keeper). That's the way I see it. Regardless of who's playing at any stage during the year, I think we've got a strong goalkeeping squad and every week's a selection battle.
"I'm not taking anything for granted. Head down, bum up and get on with it. Keep working hard and the next target is the FFA Cup game and then into the season proper in two months."
Redmayne said Covic, who will play for Perth Glory this season, had done a great job for the Wanderers and football at large.
"Absolutely, I mean he's been fantastic, not only for the Wanderers but for the game as well in raising awareness for Australian football throughout Asia," Redmayne said.
"He's a big loss to the club, but one person's loss is an opportunity for someone else and like I said before I'm one of three goalkeepers and we're vying for an important role in the starting 11."
Asked what the message to him was from Popovic, Redmayne replied: "When you get your chance, you've got to take it.
"Hopefully, I took a little step forward in our first FFA Cup match, but having said that every week is a new week and the old cliche that a week is a long time in football is very true.
"So you've just got to keep working hard and take it one week at a time. I'll keep training hard and looking at things on the video to see what I can pick up on and use to try to improve my game."
Redmayne played 48 A-League games for Melbourne Heart and then City, spread over three seasons, before joining Wanderers. Before that he played two for Roar and three for his original club, Central Coast Mariners.
Bouzanis had spent most of his senior career playing in Europe before joining Wanderers last season. He played five A-League games as the workload was spread around due to the heavy schedule the team had in the ACL as well as the A-League.
With no obvious number one at this stage the pair are bound to continue pushing each other hard all through the season in the battle for the top spot.
