Complex sentence: He stayed at York for the rest of the season but after the club was relegated to the Conference National at the end of the 2003--04 season, he joined Conference champions Chester City on a two-year contract.
Split into simpler sentences: He stayed at York for the rest of the season but after the club was relegated to the Conference National at the end of the 2003--04 season he left the club. He then signed for Conference champions Chester City on a two-year contract.