Up to his appointment as Cabinet Secretary, Huw was Chair of the Legislation, Justice and Constitution Committee and a member of the Climate Change, Environment and Infrastructure Committee.
Hyd nes iddo gael ei benodi yn Ysgrifennydd y Cabinet, bu'n Gadeirydd y Pwyllgor Deddfwriaeth, Cyfiawnder a'r Cyfansoddiad ac yn aelod o'r Pwyllgor Newid Hinsawdd, yr Amgylchedd a Seilwaith.