Getting ahead in life has fallen out of fashion lately.
Literal
Success-in-life [quotative-といった] matter [topic-は], recently [topic-は] unfashionable became [agreement-ね].
立身出世 is a 四字熟語 meaning 'rising in the world / success in life.' はやらなくなった (has stopped being popular) uses はやる (to be in fashion) + なくなる (to cease). The sentence reflects a cultural shift away from career-focused values.