[citation needed] Between 1975 and 1981, Rapley was a scientist on NASA's Solar Maximum Mission, and was then a lecturer at the Department of Space and Climate Physics of University College London from 1981 to 1987.

[4] In 1994 whilst on a sabbatical at NASA's Jet Propulsion Laboratory he contributed to the design of the Cassini RADAR instrument to study Saturn's moon, Titan.

[citation needed] From 1995 to 1997 he was Executive Director of the International Geosphere-Bisophere Programme, heading up the Secretariat hosted by the Royal Swedish Academy of Sciences in Stockholm.

[2][3] During his time as Director, he helped Al Gore with the "Live Earth" concert (7 July 2007) by arranging for the Rothera Research Station's in-house band, Nunatak, to perform in Antarctica as part of the event.

[5] Rapley co-wrote a one-man play 2071 with playwright Duncan Macmillan, which he performed at London's Royal Court Theatre in November 2014, continuing to Hamburg and Brussels.

In October 2021 Rapley resigned from the Science Museum Group's Scientific Advisory Board over the issue of gallery and exhibit sponsorship by oil and gas companies, citing; "The reality of the climate crisis, the need to abolish fossil fuels as quickly as possible, and analyses such as the recent Carbon Tracker Report which bring into question the commitment of the oil and gas companies to do so".