The nephew of former Wrexham manager Billy Morris, Elfed joined Wrexham in May 1960 after starting out with his hometown club of Colwyn Bay.[2] Two years later he moved to local rivals Chester, where he was to spend the majority of his professional career.
Morris scored 69 league goals over the next six years, leaving him as the club's fourth highest Football League scorer in their history.[3] 24 of them came in 1964–65, when Morris and fellow attackers Jimmy Humes, Mike Metcalf, Hugh Ryden and Gary Talbot all managed at least 20 goals each in league and English cup matches.[4] Morris scored an identical tally the following season, amid rumours he would be leaving for a bigger club.[4]
Away from football, Morris became a successful insurance agent in the Colwyn Bay Area and afterwards ran his own entertainment agency in Colwyn Bay.[2]