He's gotten famous and he's putting on airs about it.

Literal

Famous become-[past-so-ので] [honorific-お]-high-[adverbially-く] stop-[ongoing-contracted-てる]-[explanatory-んだよ].

お高くとまっている is the idiom お高くとまる ('to put on airs, be snobbish, be stuck-up') — literally 'to stand on high ground.' The お- adds ironic honorific distance, as if mimicking the snob's own pretension. 止まる here means 'to stand, perch, come to rest.' Catty and colloquial, often used behind someone's back.