Palmer later form the super group Power Station. Via Wikipedia:
"Duran Duran went on hiatus, and their guitarist Andy Taylor and bassist John Taylor joined former Chic drummer Tony Thompson and Palmer to form Power Station. Their eponymous album, recorded mainly at the New York recording studio for which the band was named, with overdubs and mixing at Compass Point Studios in Nassau, Bahamas, reached the Top 20 in the UK and the Top 10 in the US. It spawned two hit singles with "Some Like It Hot" (US #6) and a cover of the T.Rex song "Get It On (Bang a Gong)", which peaked one position higher than the original at US #9. Palmer performed live with the band only once that year, on Saturday Night Live. The band toured, and played Live Aid, with singer Michael Des Barres after Palmer bowed out at the last moment to go back into the recording studio to further his solo career."
A heavy smoker, Palmer died of a heart attack in Paris in 2003 at age 54.