Kellaway began his career with
Aberystwyth Town, making his debut during the 2003–04 season. He went on to make over 100 appearances for the club and also featured in the 2009
Welsh Cup final defeat to
Bangor City. In May 2010, having been named in the 2009–10
Welsh Premier League team of the season, Kellaway joined
Dandenong Thunder along with fellow Welsh Premier players Luke Sherbon and
Jamie Reed, making his debut in a 1–0 victory over
Hume City on 29 May 2010. On 17 August 2010, he was signed to a three-month injury replacement contract with
A-League side
Melbourne Victory to cover for
Matthew Kemp, after impressing in a trial match against the side. In July 2011, he re-joined
Aberystwyth Town. In June 2012 he moved to
Llanelli but the club folded in April 2013. He had a brief spell with
Carmarthen Town before returning to Aberystwyth Town for a third spell. Kellaway signed a new contract to carry on playing for Aberystwyth for the 2019–2020 season. He scored 9 goals in 19 games in 2018–2019 ending up as the club's top goalscorer that season. In June 2021, Kellaway joined
Cymru North side
Penrhyncoch. ==Personal life==