Blaymire was born in Leeds, West Yorkshire, England on 4 June 1982. He started his rugby league career in the Wakefield Trinity Wildcats academy before joining York City Knights in 2003, where he scored 22 tries in 50 appearances.
After impressing for York, Blaymire returned to the Wakefield Trinity Wildcats at the end of the 2006's Super League XI (Heritage № 1245). He spent five seasons at Wakefield Trinity Wildcats, making over 100 appearances for the club before being forced to retire in 2011 due to a knee injury.