Hi @Anonymous ,
Do you want to add new members to this Security Group within canvas app?
Firstly, you could share your canvas app to Office 365 Group, but this Office 365 Group must be security enabled. Please check the following article for more details:
https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/share-app#share-an-app-with-office-365-groups
If you want to add new members to this Security Group in your canvas app, I think Office 365 Groups connector could achieve your needs.
I have made a test on my side, please take a try with the following workaround:
Add Office 365 Groups connection and Office 365 Users connection in your app. Then add two Dropdown boxes to list your owned available Groups (including Security Group) and Available users in your Org:



Set the Items property of the first Dropdown box (GroupDropdown) to following
Office365Groups.ListOwnedGroupsV2().value
Set the Items property of the second Dropdown box (UserDropdown) to following:
Office365Users.SearchUserV2({top:999}).value
Set the OnSelect property of the "Add Member" button to following:
Office365Groups.AddMemberToGroup(GroupDropdown.Selected.id, UserDropdown.Selected.UserPrincipalName)
Within the GroupDropdown box, select the proper Security Group, then within the User Dropdown box, select proper User you want to add to to this Securoity Group, then press the "Add Member" button, then the selected user would be added into this Security group.
Note: I assume that you created this Security Group or you are one member of Security Group already
Please take a try with above solution, check if the issue is solved.
Best regards,