||A form of draughter used to help a fire (household) ignite.
The hastener usually consisted of a sheet of tin, large enough to cover the opening of an 'open' fire, the air ws sucked into the fire through the grate. It was a primitive form of bellows. Sheets of newspaper were also used in a similar fashion.
||Put the hastener to the fire, it's going out.
Put the hastener against the open fire to help it catch.
||Probably 'Hasten' - to quicken.
And note 'a semi-circular screen lined with tin placed behind meat roasting before the fire to keep cold air off and hasten cooking by refecting heat' (many English counties). (Wright)