An election in-between regular elections, I think. Say a member of the House of Commons dies or resigns between regular elections. There's a by-election to fill the seat fairly soon afterwards, so it isn't vacant until the next regular election.
can you please allow bye-elections as bye means lesser/near etc.
Good suggestion that's added now, as is 'special election' since this seems to be the term used in the USA.
You have a typo.
A bye election ( I don't think so ) Look at your answer here.