Ofori was linked with a move away from the Team of Choice in the current transfer window.
The Ghanaian shot-stopper was linked with a move to Orlando Pirates after the Sea Robbers technical team looking to sign a goalkeeper.
Tinkler has made Ofori his captain in the new season.
“We are going to have our match-day captain which will be Richard Ofori,” Tinkler told the club’s website.
“Like I said before, there is very little guarantee to any player that he will be in the starting line-up – that’s the type of competition we want to create.
“So selecting a captain was always going to be difficult. Richard, a national team goalkeeper for Ghana, is definitely our first-choice goalkeeper, so it made sense to appoint Richard as our match-day captain.
“Then we have the club captain. Who plays even more of an important role because he is representing the players to the club and also to me. And that person will be Nazeer Allie. Because of all his experience.”