Carrack first rose to prominence with Ace; he was the lead singer on their one hit, 1974's "How Long." After Ace broke up, he joined Roxy Music and played keyboard on two albums before replacing Jools Holland in Squeeze (1980) where he sang lead on "Tempted." After leaving Squeeze he tried his hand at a solo career and worked with Eric Clapton and Nick Lowe before joining Mike + The Mechanics. With Mike + The Mechanics he shared lead vocals with Paul Young, but sang lead on "Silent Running (On Dangerous Ground)" and "The Living Years."
In 1987, again released a solo record with some success. The One Good Reason album would reach #67 on the charts, and produced two top 40 singles -- the title cut and "Don't Shed a Tear," which would hit #9. By the by, "Don't Shed a Tear" was written by professional songwriter Eddie Schwartz, perhaps best known for Pat Benatar's "Hit Me with Your Best Shot."
The video for "Don't Shed a Tear" was directed by Peter Care, who would go on to direct a boatload of videos for R.E.M. and Belinda Carlisle. (He also directed Banarama's "Venus" and "Rise" by Public Image Ltd.) The model/actress is Kendal Conrad, who has since left the industry, I believe.
Carrack remains active in the industry to the present day and has seemingly worked with everyone. (OK, slight exaggeration, but he has worked with a ton of folks).