This is one of the most common situations we are asked about, and one of the hardest for a CEO to handle well. There is a good person inside, everyone likes them, and they are two years short of the role.
First, define "not ready" precisely
Not ready is usually a feeling. Turn it into a list. Against the role as it needs to be, where exactly are the gaps? Scale? Board exposure? A functional area they have never run? Commercial judgement? Most internal candidates have one or two specific gaps, not a general shortfall.
An external benchmark helps here. If the market would offer you people with the same gaps plus a learning curve, the internal candidate is readier than you think.
Option one: appoint, with structure around the gaps
Works when the gaps are narrow and the organisation can absorb some risk. A Chair or non-executive who mentors on Board exposure. An experienced number two in the area the person has not run. A clear review point at twelve months, agreed with the candidate up front.
Option two: bridge
Works when the gap is real but the candidate is the right long-term answer. An external appointment on a defined term, with the internal candidate as deputy and a stated plan for the handover. This needs honesty with the external hire about what they are being brought in to do; some senior people are happy to build a successor, and some are not.
Option three: search, with the internal candidate in the process
Works when the gap is wide or the organisation cannot afford the risk. The internal candidate goes through the same assessment as the external shortlist. If they lose, they have lost to evidence, which most people can accept. If they win, the organisation has the appointment and the proof.
What not to do
Do not leave the person as acting head for eighteen months while the Board makes up its mind. It is the most common outcome and the worst one: the person does the job without the authority or the pay, the organisation learns nothing, and the good ones leave.