expression, i-adjective
not feeling like doing ...; having no intention of ...
Used after a verb to express a lack of desire, mood, or intention to do that action. Often appears as 〜する気はない or 〜しようという気はない.
今は外に出る気はない。
I don't feel like going out right now.
彼は謝る気はないようだ。
He doesn't seem to have any intention of apologizing.
気がない is a more general expression meaning 'have no interest' or 'not care about something', while 気はない specifically follows a verb and emphasizes the lack of intention or mood for that action.
A fixed expression combining 気 (mind, spirit, feeling) with the topic particle は and the negative form ない, literally 'as for the feeling, there is none'. The derivation is transparent from its components.