Not in the same sense as some of the other tools can.
You will have to first export the list of contacts that belong to the contact group, then create new contact/contact group for the users with whom you would like to share.
gam user <username> print contacts contactgroup id:<contactgroupId> todrive
then you can do
gam csv gsheet <AdminEmail> <fileId> <sheetName> gam user <username> create contact <contactAttribute from Sheet> contactgroup <contactgroupName>