who has been elected
or otherwise chosen
as the new president
of an organization
, but whose term in office has not yet begun.
In US government, the period during which the president-elect usually prepares for the transition is also the lame duck period of the outgoing President.
Some non-governmental organizations (wisely, IMO) make president-elect an official position, prescribing a term of a year in which the president brings the president-elect up to speed.